Evaluate the integral. 3) S- dx x/ 16x2 - 7

Q: /2 + x dx

A: The solution are next step

Q: 2x Use substitution to evaluate the integral dx (x² + 3)°

A: We have to apply rules of integration to solve the problem Power rule: xn =( 1/n+1)(x)n-1

Q: b) Evaluate the integral by parts. S, x* Inx dx

A: given I= ∫1ex4 ln x dxby using LIATE rule we can rewrite integral as    I= ∫1e ln x   (x4) dx     =…

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A:

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A:

Q: Evaluate the improper integral 2). L, xe-** dx

A: To solve the improper integral

Q: X. S 2x4 x³x²+x-1 - dx

A: Since multiple questions are asked I am answering first question

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A:

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A: The integration by parts formula is ∫udv=uv-∫vdu

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A:

Q: Evaluate the integral. x sec? (7x) dx + C

A: We have to find integral.

Q: Sx²e2x*dx `x²e?

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: We solve this integration with the help of some basic formula of integration and sone basic…

Q: Which is NOT included in evaluating the integral? 2 + Vx) dx а. dx

A: The answer of the following questions is given below...

Q: Evaluate the integrals:

A:

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A: Evaluate the integral.     ∫576dx

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A:

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A:

Q: 4 + V16-x? dx 3 2

A:

Q: Evaluate the integral: - c s 4x)dx

A:

Q: Evaluate the integral.

A: Given integral is ∫1x21+x2dx

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A:

Q: Evaluate the integral ∫dx / √(a2+x2)3.

A:

Q: dx ,2 /9 – x² 2

A: Solution

Q: The improper integral| dx x²+4x+8

A:

Q: Evaluate the improper integral : S 4x³e¬9*, dx

A:

Q: Evaluate the integral using an appropriate method. J = 3 22+5+6 dx

A:

Q: Evaluate the improper integral : [° 6x°e¬9æ° dx

A: To solve this question assume 6x^5 = t

Q: Evaluate the improper integral. ∞ ∫dx/((x^2) − 1) 2

A: Given improper Integral

Q: Evaluate the integral. dx 2 (a² + x²)3/21 a>

A:

Q: Evaluate the integral of (x^2)/(x^2 + a^2)^3/2 dx

A:

Q: 5. Evaluate the integrals using appropriate substitution., a. x*/5+x* dx b. f coszdx os-dx 7x2 +…

A:

Q: Evaluate the integral. 8. dx 2

A: dxndx = n.xn-1 . ∫un du = un+1n+1+C

Q: Evaluate the integral. /x + c dx

A:

Q: 3.1 dx x² – 25

A:

Q: a) Evaluate the integrals using a dx i) S16x2 1+16x?

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Evaluate the integral: | x(4 - x)3/2 dx'

A:

Q: Evaluate the integral. | 6 x/2(3 + x3/2)7 dx II

A: we will take x^3/2+3=u and then solve it in u and then substitute the value of u in the equation at…

Q: 4 -dx xln?x 00

A:

Q: Evaluate the integral. - 20* + 4cosx) Sx²(x+5)°dx

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Q: Evaluate the integral. 50x In(x) dx : + C

A:

Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

A:

Q: Evaluate the integral J*(x*-1)°dx by using substitution.

A:

Q: Evaluate the integral. '8 xet dx (1 + x)?

A:

Q: Compute the integral by algebraic substitution: ∫7/2+√x-4 dx

A: We need to compute the integral ∫72+x-4 dx Now, using the property ∫a fx+bgx dx=a∫ fx dx+b∫gx dx…

Q: Evaluate the integral.

A: Now consider,

Q: Evaluate the integrals. ∫y2/(y3 + 27)dy

A: Given: ∫y2y3+27dy

Q: Evaluate the integral. ,2 X- + x + 1 dx o (x + 1)2(x + 2)

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.