J. x sin 3x² dx

Q: evaluate the definite integral.

A: We rewrite the given integral using the double angle formula

Q: Verify the value of the definite integral, where n is a positive integer.

A:

Q: Evaluate the definite integral. (Assume a > 0.) 'al/5 x°Va? - x10 dx

A:

Q: dx I = a² +x²

A: Given query is to find integration of the expression.

Q: 25. Evaluate the following definite integrals. c) LIVII – x dx

A:

Q: Find the indefinite integral.

A: To find, ∫8x cos2x dx We use the following formulae ∫c f(x) dx=c∫f(x) dx∫xn dx=xn+1n+1∫cos(ax) dx…

Q: Evaluate the following integrals. 2. ∫[sin(ln?)+cos(ln?)]^2/? ??

A: Solving 2).

Q: Find the indefinite integrals: (a) S dx x+1 + C. (b) S da = 23 x2+1 =

A: SOLUTION-

Q: Find the following indefinite integrals.

A:

Q: d) V1+x? dx

A: Consider the provided question, We need to evaluate the definite integral ∫01 x31+x2dx

Q: Evaluate the following indefinite integrals. sin? 5x cos? 3.x dx

A:

Q: x+ dx sin? 2

A:

Q: S cos(3=)dz

A:

Q: D) Calculate the following definite integral: [* (/{√x - 1) dx

A:

Q: Evaluate the indefinite integral 5e^5x*sin(e^5x) *dx

A:

Q: sin (x) cos/2 (x)dæ sin (x)dx

A: To find the integration

Q: 4 sec?x dx 2. tan?x+ 2tanx +5

A: topic - indefinite integral

Q: Evaluate the indefinite integral sin Væ dx. Answer:

A:

Q: dx I = е. a² +x²

A:

Q: ii) sin5x cos*x dx

A:

Q: Evaluate the definite integral. 1/2 (sin x)16 dx xp

A:

Q: Find the following indefinite integral: ∫ x1/3 sin(x4/3-8) dx

A: Given,            ∫ x13sin(x43-8)dx

Q: Evaluate the definite integrals

A: We substitute cosx =t and sinxdx=-dt

Q: Which of the following is one of the correct/convenient steps to evaluate cot-4dx which will yield…

A:

Q: Refer to the definite integral to answer the following questions 3 1² (2²) (x²) dx

A:

Q: 1. Evaluate the following definite and indefinite integrals. a) St sec2(t?) tan*(t²) dt

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL  BE ANSWERING ONLY THE FIRST…

Q: Evaluate the indefinite integral. 3e* sin(e) de

A: Solve the integration by substitution method

Q: Evaluate the definite integral.

A: To evaluate  ∫01sinh2xdx

Q: Find the following indefinite integral. I dx x2 + 9

A: From the given problem:   I=∫xdxx2+9...(1)   Let,   x2+9=t   To differentiate with respect to x.…

Q: Evaluate the integral e^2x sin(4x)dx from 0 to pi.

A: Use integration byparts again and again you will get again an integration in the form of I ...as I…

Q: b) Calculate the following definite integral: [*(√x - 3) dx

A:

Q: 14. E sin x dx cb

A: According to the guidelines, I am answering first question. Please repost the remaining. Explanation…

Q: Solve the following indefinite integrals. (a) cos x -dx sin? x (b) sin- cos cos,dx (c) sin) dx cos

A: (a) To find: The indefinite integral of . Calculation: Substitute in . Substitute in above…

Q: 3. Find each of the following integrals using any suitable techniques: (d) sec® 4x tan² 4r dx

A:

Q: TT sinx sin 2x dx 2 cos x

A:

Q: EVALUATE THE INTEGRAL

A:

Q: (1) sin?x dx

A:

Q: sin 2x dx .2. 1 + cos?x

A: Given, ∫sin2x1+cos2xdx   We have to evaluate the indefinite integral

Q: e +1 dz e + z

A:

Q: Find the indefinite integral. sin° 70 v cos 70 de

A: Given,           ∫sin37θcos7θdθ

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

A: (a) To integrate: ∫ex2dx We know that, ex=1+x+x22!+x33!+⋯⋯=1+x+x22+x36+⋯⋯ Now, ex2=1+x2+x42+x66+………

Q: Evaluate the following indefinite integral. -x-2 (a) dx dx (b) cos 0 sin Od0

A:

Q: Evaluate the following definite integrals.

A: I =  ∫01xsinπx.dx  ................(1)we know ∫abf(x).dx = ∫abf(a+b-x).dx

Q: Evaluate the definite integral. m/2 5 cos(x) sin(sin(x)) dx

A:

Q: Evaluate the definite integrals

A: Given,

Q: Evaluate the following integrals: 1. So? 2. cos 2x dx

A:

Q: Evaluate the definite integral. "Tt/2 " d(sin x)? dx = (sin x)2 dx =

A:

Q: Find the integral for the following functions: - sin(x). esec(x) 1). 1) S cos (x)

A:

Q: Refer to the definite integral to answer the following questions: 4 [*(16-x²) dx

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 34. cos(m/x) dx

A: