Evaluate the integral. (Use C for the constant of integration.) 5x cos(4x) dx

Q: 5. If a and b are positive constants, evaluate the following integrals: ,-bx e-ax -e -dx; (a) (b)…

A: The objective is to evaluate: ; where a and b are positive constants.

Q: Q2. Use Integration by parts to evaluate the following integrals Sear cosbx dx

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Q: 14 Find the integrals using integration by parts. a. fx(x + 4)°dx c. fr'e"dr

A: As per our guidelines I am solving only first three parts of the question please resubmit the other…

Q: Evaluate the integral. (Use C for the constant of integration.) A) x cos(2x) dx B)e6θ sin(7θ) dθ

A: here we evaluate the integral      (A)   ∫ x cos (2x)dx     (B)  ∫ e6θ sin (70) dθ

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

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Q: a) Integrate the following expressions with respect to x. Then, find the value of the function…

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Q: Solve the following integral using the integration by parts method. (i) |x² sin mx dx (ii) e* cos 3x…

A: We can find the integration using by parts method

Q: II. Perform the integration. sinh? (e¬) dx eª cosh(e-¤) 2 4.

A: We have to find value of given integral.

Q: 2 b) S dx e-x +1

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Q: 2,31 dx

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Q: 2 dx a) Evaluate the integral by completing the square and using a substitution 2 x2-6x+10

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Q: I. Evaluate the following integrals. •ln 2 #3. e2" sec-(e")dx

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Q: a) Evaluate the following Integration by parts for definite integrals. i) So xe-s*dx ii) 12 Sin-'dx

A: The given integration is  I) ∫01xe-5xdx II) ∫032sin-1xdx

Q: sinx dxdy By reversing the order of integration, the value ofl is equal to: O None of these O et1

A: We will change the order of the integration. We will set the limits of x free and set the limits of…

Q: T 15 dx The integral is equal to

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Q: Evalute the following integrals. (1) /; COs x -dx. 1+ sin? x 2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral. (Use C for the constant of integration.) e60 sin(70) de

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Q: Evaluate the integral. •3 dx x4/x² + 3 NOTE: Enter the exact answer.

A: Explanation of the answer is as follows

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) sin…

A: see below the calculation

Q: Find the integrals below. a) J(2x + 3)* dx b) (x?(x³ + 3)6 dx

A: Integrate. ∫2x+34dx=2x+355×1ddx2x+3+C=2x+355×12+C=2x+3510+C

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dx,…

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Q: a) FIND the following integrals: 2m i) S"(cos x +| cos x |)dx (ii) S

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Here we have to find the Given integral using substitution method.

Q: Decide on what substitution to use, and then evaluate the given integral using integration.) x² dx…

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Q: Evaluate the integral. (Use C for the constant of integration.) ∫ e4θ sin(5θ) dθ

A: we have to find the value of integral ∫e4θsin(5θ)dθ to find the value we use the formula ILATE which…

Q: Q2. Use integration by parts to evaluate the following Integral 2 COs x² dx

A: GIVEN : ∫ x3 cos x2 dx

Q: dx The integral can be rewritten as 1- x

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: The given integral is,

Q: 3. Using the Trapezoid and Simpson's rules, solve the integral below. a. I = x' In xdx 0,8 b. 1=…

A: To find the value of the integral by trapezoidal or Simpson rule if we take more number of…

Q: x3 + 3x + 1 dx| J (x + 1)²(x – 2)² Find A, B, C, and D then find the integral?

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Q: Evaluate the integral.

A: ∫x24-x232dx Put, x=2sinθ⇒1=2cosθ·dθdx⇒dx=2cosθ·dθ

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: To calculate the integral

Q: dx The integral can be rewritten as 1-x

A: Given that the integral  ∫-∞0dx1-x We can write this integral  limx→-∞∫s0dx1-x

Q: dr Evaluate the integral / dx. sin x cos x

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Q: cos? x dx x2 ex 3) Find the integrals if there exist i) Sozdx , ii) x2

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Q: Evaluate the integral ∫e^(2x) sin(e^x) dx, by first making a substitution and then using integration…

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Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

A: To find out the integral.

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Consider the expression 3x2-2=u. The power rule of differentiation states that d dx(xp)=pxp-1, where…

Q: Evaluate the integral

A: ∫1+x2xdx Put, x=tanθ⇒1=sec2θ·dθdx⇒dx=sec2θ·dθ

Q: Evaluate the integral. (Use C for the constant of integration.) cos 30 de

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Q: d) S cos³x sin*x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) (5 + e) dx e

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Q: Evaluate the integral. (Use C for the constant of integration.) e-0 cos 80 d0

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Q: dx. (xVz - 5)2 dx.

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Q: b) Evaluate the integral x? e* dx.

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Q: 3. Using the Trapezoid and Simpson's rules, solve the integral below. a. I= [x In xdx 0,8 b. 1=…

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Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

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Q: First make a substitution and then use integration by parts to evaluate the integral 7x°e" dx Note:…

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