Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

Q: Evaluate iterated integral.

A: Given, ∫12∫121xdx dx

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Q: Use the tabular method to evaluate the integral - 2x – 1) cos(4x)dx

A: Introduction: Tabular integration is a technique for quickly integrating many parts in a row. One of…

Q: 2 dz dx dy +2 Volume 2y 9-y?

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Q: Can the integrations in (a) and (b) both be correct? Explain. dx dx -cosx + C a. VI - x V1 – x² /-…

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Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

Q: To integrate y3xdx we apply integration by parts and in the form u dv, u is set as:

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Q: Evaluate iterated integral.

A: Given, ∫01 ∫36 xx2+3y dx dy

Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: Evaluate the integral dx (6х + 5)? y making the appropriate substitution: u = dx (6x + 5)2 II

A: Given query is to find the integral.

Q: | dx X æ /æ2+100

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Q: The vahe of the integral fx*dx with step length 0.5 using Trapezoidal's nule is a) 0.375 b) 0.875 c)…

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Q: Evaluate iterated integral.

A: Let the given integral be I - I = ∫39∫57 xy+y5dx dy  Let's first integrate with respect to x (we…

Q: Evaluate the triple integral S" S, sin y² dz dy dx.

A: We need to find the triple integral ∫03∫0π∫0ysiny2dzdydx. So,…

Q: Use u-substitution to evaluate the integral. 3 + 5 Vx dx 3 2 + 5 Vx dx =O

A: Given query is to eveluate the integral.

Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: Evaluate | VF In(r)dx by using integration by part.

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Q: dx dy y? 0,

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Q: Consider the integral sin-(5x) dx: Applying the integration by parts technique, let U = and dv dx…

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Q: evaluate using Integration by Parts.

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Q: 1. Integrate using Integration by Parts: I sec? x dx

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Q: aluate the iterated integral. || 5x²sin(y) dy dz dx =

A: Given: ∫0π∫05x∫0xz5x2sinydydzdx

Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

Q: Vx3+V4x+8 dx 2 vä ( \x²)

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Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Calculate the double integral. 7x sin(x + y) da, R = [0, * [0, =]

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Q: Evaluate 9 + y² dy dx by first interchanging the order of integration. Sketch the region of…

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Q: Calculate the iterated integral. 12 2ex + 3y dx dy

A: Consider the inner integral, name it as I1 Take the constant 2 out of the integral sign.

Q: Evaluate the integral: + 6 dx = %3D

A: Find the integral by using substitution method

Q: Evaluate the line integral - y² dx, where C is the square cut from the first quadrant by the lines x…

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Q: the double integral dy dx Evaluate 2.

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Q: Evaluate the double integral (1+ r² + y?)² dy dx

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Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: Evaluate the iterated integral. 2ye-* dy dx 12

A: Given that, ∫25∫1x2ye-xdydx we have to find the value of this integral.

Q: Evaluate the integral ex 2e-2x - 3e2x | Arcsin V6e2x 2 A V3 +C ®Arcsin l V3e2x +C B © 2/2e-2x - 3e2x…

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Q: Vx 3+4x+8 dx 2 vã (Vx?)

A: The given function is x34+4x+8xx23 We have to identify u and du and the form of the integral of this…

Q: find the inderinite integral it 2. dx 7-3x3

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Q: Sketch the region of integration, then change the order of integration in 4 16 order to evaluate the…

A: In change of order of integration process, the integration dx dy is changed to dy dx, that is if…

Q: The value of (4xy- (sinx)³)dx + (x² + y9)dy (Correct to ONE decimal place) where C is the region…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. To evaluate the given…

Q: Approximate∫b,a f(x)dx by computing Lf(P), Uf(P), left sum and right sum of the following integral:…

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Q: Use the specified substitution to find or evaluate the integral.

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Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: a. Sx² e3*dx b. St sin t dt

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

A: Given:           ∫e2xe2x+3ex+2dx

Q: Consider the integral sin-'(5x) dæ: Applying the integration by parts technique, let U = and dv dx…

A: Integration by parts is expressed as If I=∫f(x)⋅g(x)dxThen I=f(x)∫g(x)dx  - ∫ddxf(x)⋅∫g(x)dxdx Here,…