Use the midpoint rule with 4 rectangles to approximate (x? – a*) dx: The integral is approximately

Q: by using the double integration, find the area that lies inside the curve r= (8cos e) and outside…

A: Given: The curves r=8cosθ    and r=4

Q: Evaluate the integral using tabular integration by parts. 4 x° V2 x + 1 dx +C

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Q: Evaluate the integral by making an appropriate change of variables. / 9 sin(49x2 + 64y2) dA, where R…

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Q: of unit circle , when F(r)

A: The function given is Fr=-x,-xy here r is the radius of circle ,r=x,y→dr=dx, dy. Apply Green's…

Q: Evaluate the integral by reversing the order of integration. '3 5ex dx dy J3y

A: We have to evaluate the integral by reversing the order of integration.

Q: Find the integral for f dx when n-4 by using Trapezoidal rule for five digits

A: Using  trapezoidal rule,Area=h2y0+y4+2y1+y2+y3Let fx=xx2+2, where, h=b-an=2-14=0.25          a=1,…

Q: Evaluate the integral using integration by parts. Sxsin x sin (8x)dx Jrsi x sin (8x)dx =

A: Integration

Q: use a definite integral to find the area of theregion between the given curve and the x-axis on the…

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Q: use the integration by parts to evaluate the intergral  x In2 x.dx

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Q: Use the Midpoint Rule with n = 3 to approximate the integral 16 | (- 10x + 2x2) dx 10

A: In this question we will use basic of calculus i.e concept of midpoint rule to approximate the…

Q: Evaluate the integral by making an appropriate change of variables. 4 sin(81x2 + 49y²) dA, where R…

A: To Evaluate: ∬R4sin81x2+49y2dA,R is the region in the first quadrant bounded by the ellipse…

Q: Evaluate the inner integral by Simpson's rule with n = 5 and outer integral by rectangular rule with…

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Q: Use the 4-segments multiple Trapezoidal rule to estimate the integral L VI+ z*dz

A: Given that  The integral is  To find the integral by using trapezoidal rule

Q: Approximate the integral to three decimal places using the indicated rule. 308 -dx; trapezoidal…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(æ) dz…

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Q: 10 3. sec x dx

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Q: Use the Midpoint Rule with n = 4 to approximate 2x the integral 1 dx to three decimal place.

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Q: Evaluate the integral.  integral y 3 sqrt (y 2 +1 )dx

A: We have to evaluate the integral: ∫y3y2+1dy We will use substitution method to solve this integral…

Q: Use the Midpoint Rule with the given value of  n toapproximate the integral. Round the answer to…

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Q: x sec (3x) tan (3x)dx

A: The given integral is ∫xsec3xtan3xdx. We know the integration by parts formula:…

Q: Find the integral of (x)(arctan x) dx,

A: Given: evaluate

Q: 2x dx Vx+3

A: Topic = Integration Use∫xn dx=xn+1n+1+C

Q: Use a table of integrals to find the length of the curve y = x² from x = 0 to x = 2. %3D

A: The equation of the curve is given as, y = x2 we need to find the length of curve in the interval x…

Q: By using double integrals, find the area of the regions enclosed by: (a) y=4-x² and y=3x (b) y=sinx…

A: Area of region between two curves.

Q: sketch, reverse and evaluate the integral dy dz 15

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Q: Use trapezoidal rule to estimate the the integral. V + Adx n=6 a) 2.75

A: the given integral is ∫14x2+4dx given n=6 therefore  h=b-an=4-16=36=0.5

Q: Se* sin x dx

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Q: ydy (y–1)*

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Q: Use the midpoint rule with the given value of n to approximate the integral. (Round your answer to…

A: Use the Midpoint Rule with the given value of n to approximate the integral.

Q: Evaluate the integral using integration by parts. 9x° e 2x dx 2x dx =

A: Given, ∫9x3e2xdx

Q: Use the Midpoint Rule with n=3 to approximate the integral 6. %3D (8x + 6x2) da

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Q: Approximate the integral to three decimal places using the indicated rule. 1.6 sin(x2) dx;…

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Q: Use the Midpoint Rule to approximate the integral 15 (-læ – 3a?)da with n=3.

A: Given,  ∫715(-1x-3x2)dx

Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: Given: ∫x3x2+13dx

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

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Q: Evaluate the integrals below: etanx sec² x 3. a) V(1 – (elanx )2 :. dx, b) / cot5x. dy

A: We need to integrate of the following integrals.

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(x) dx…

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Q: find the relation error use the trapezoid rule to approximate the definite integral. Use n=4 Inx dx

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Q: Evaluate the integral by using u-substitution and changing the limits of integration. 3x dx J, ex++1

A: ∫-103xex4+1dx Let say, u=x4 Therefore, du=4.x3.dx  ⇒ x.dx=du4x2=du4u. x=-1 ⇒u=1x=0⇒u=0 Therefore,…

Q: Approximate the integral to three decimal places using the indicated rule. 9 cos(x) r0.9 dx;…

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Q: sketch, reverse and evaluate the integral dy dx

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Q: First make a substitution and then use integration by parts to evaluate the integral. dx

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Q: Evaluate the integral by making an appropriate change of variables. 2 sin(25x2 + 36y2) da, where R…

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Q: Use the Midpoint Rule with n = 3 to approximate the integral %3D - x + a?)da

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Q: Evaluate the integral using tabular integration by parts. 8 x³ V2 x + 1 dx +C

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Q: Evaluate the integral using tabular integration by parts. 2 x³ /2 x+1 dx +C

A: Recall the tabular integration by parts

Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Use the trapezoidal rule with n=6 subintervals to approximate the integral 1 to 4  ln(x+sqrt(x)) dx.

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Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: Evaluate the integral using tabular integration by parts. 5 x° V /2 x + 1 dx +C

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Q: Evaluate the integral by making an appropriate change of variables. 9 sin(81x2 + 64y2) dA, where R…

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Q: Evaluate the integral by making an appropriate change of variables. 7 sin(25x2 + 25y²) dA, where R…

A: Double integral evaluation, conversion to polar coordinates

Q: use the midpoint rule n=5 to approximate  integral 1 to 2 (1/x) dx

A: To find: The approximate integral of ∫121xdx with mid point rule n=5. Concept used: If fx is…