3 a2 Calculate the integral: da (*- 9)2 (x+ 9)

Q: (6x + 4x? -90x - 64 da Consider the indefinite integral x2 16 -

A: I = ∫6x3+4x2-90x-64x2-16dx as Numerator degree is greater than denominator degree, So, on dividing…

Q: Evaluate the integral J dx V4-9х2 3.

A: This question is related to integration.

Q: Calculate the integral

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Q: Evaluate the integral. 43tan“x - secx dx %D

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Q: Evaluate the integral (use the substitution): е x+1 xp- (x + 1)2 a.

A:

Q: Evaluate the indefinite integral: ∫(18t5 − 10t4 − 28t) dt

A: Given the indefinite integral: ∫18t5-10t4-28tdt

Q: Evaluate the integral.

A:

Q: Consider the integral -8e-2' dt If the integral is divergent, type an upper-case "D". Otherwise,…

A: Given: ∫-∞-1-8e-2tdt

Q: da Vx2 +1 Evaluate the integral

A:

Q: -14 dx 4 -2 x+2

A:

Q: Evaluate the integral. х — 1 dx x2 - 7x - – 8

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Q: 1= [3y/7-3y° dy

A:

Q: Evaluate the integral. 2 + du -

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Q: Find the Integral by using the substitution method.  x(7-x^2)^1/2

A: Given query is to find the value of the integral.

Q: Evaluate the integral: a² /1+ 9=*dz

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Q: Evaluate the integral. (Use C for the constant of integration.) x² - 64 dx - +8

A:

Q: 12x? Evaluate the integral: - - x² xp-

A:

Q: 9. dt 2 -4

A: ∫9t2-4dt=9·∫1t2-4dtLet u=\arcsec12t=9·∫secudu=9lntanu+secuSubstitute back…

Q: Evaluate the integral * (2* – 4)" de by making the substitution u a6 – 4. - + C

A: We know that  ∫xndx=xn+1n+1+C We make the substitution u=x6-4du=6x5dxdu6=x5dx

Q: Evaluate the integral -9 dx Vx² + 16

A:

Q: Evaluate the integral by making the substitution u = x° – 7. + C

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Q: Evaluate the integral */2 10z csc (r) dr /4

A:

Q: Calculate the integral ∫dx / √(x2−8)3.

A:

Q: Evaluate the integral J x3 dx V64-x²

A: let I=∫x364-x2dx

Q: Evaluate the integral (3x +y)dA {(x,y)|-2sy53, y -35xsy+3}.

A: It is asked to evaluate the integral, the region D is defined as, D = {(x,y) | -2 ≤ y ≤ 3,  y2-3 ≤…

Q: Use the substitution u=x2+4 to evaluate the indefinite integral below. 2x(x2+4)8

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Q: Evaluate the integral. dx J2 (x² – 1)3/2 -Csc O

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Q: 64x2 – 25 dz Evaluate the integral:

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Q: Evaluate the integral. -1 4 6y5 dy + -2

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Q: 17 Evaluate the integral: SERV - dx x²√x² + 25 (A) Which trig substitution is correct for this…

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Q: Evaluate the integral.

A: To evaluate ∫1x3-1dx

Q: evaluate the integral.

A:

Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: 4x4 +1 dx 2г3 + х? —

A: We are given the Integral:∫4x4+12x3+x2-xNow , using long Division…

Q: Evaluate the indefinite integral dx +C. %3D -99+20x-x2

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Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

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Q: yz dxdzdy -126 -84

A:

Q: Evaluate the integral. 8 V1-t2

A: We have to evaluate the integral: ∫02281-t2dt We know the formula of integral, ∫1a2-x2dx=sin-1xa+c…

Q: Evaluate the integral by making the substitution u = x – 6.

A: Given,           ∫x2x3-637dx ; by making the substitution u=x3-6

Q: [²₂ 0 y√2y - y²dy

A:

Q: 3) Use long division to evaluate the indefinite integral f „s dx.

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Q: 8a Evaluate the integral by making the appropriate substitutions. Write your solution as a single…

A: Integration of the function helps to find the required value of the given expression. Integration…

Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: I = 2т dxdydz Is

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

A:

Q: Evaluate the integral: -2 y√2y-y²dy

A: A detailed solution is given below

Q: Evaluate the integral fos√²²-1 f√²-1. 2x by first rewriting in the order dxdy. Enter the numerical…

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Q: dz convergant 5Joj Is the Integral or divergent. I

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Q: Evaluate the integral |-1|2 – 4z| de

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Q: dx, Evaluate the improper integral : [° 6x³e-3x°

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.