b) The number t can be evaluated by the following integral. V1-x2 dx = Tt

Q: 3tan a sec? x dx (4+3tan=)* 2

A:

Q: Use the substitution formula to evaluate the integral. S'ia dx (Hint: simplify first) 1 2 11 22

A: Solve the following

Q: Evaluate this integral. x? (a? – x²)3/2 dx

A:

Q: Evaluate the integral. 17 dx 2 Vx² – 1 - NOTE: Enter the exact, fully simplified answer.

A: Let's find.

Q: Which value has the following integral I = 45 -45x2 e dx

A:

Q: Evaluate the following integrals. Show all the necessary solutions. 2. y In?(1 + 3*) dy 1 + y²

A: I=∫y ln7(1+y2)(1+y2) dyI=∫ y ln(1+y2)7(1+y2) dyln(1+y2)=t1(1+y2) (2y) dy =dty(1+y2) dy=dt2

Q: Write the definition of line integral and apply it to solve the following integral: z² dz Such that…

A:

Q: Evaluate the integral. dx a > 0 + x²)3/2? 4 Jo (a2

A: given, 4∫0adxa2+x23/2 , a>0

Q: 2. Use a substitution to change the integral into one found in the table of integrals, then…

A:

Q: Use the value of the first integral I to evaluate the two given integrals. 3 9 4 3 (8х-2x3) dx b. J…

A:

Q: Evaluate the multiple definite integral J, J. zr²sinu du dr dz

A:

Q: Which one of the following integrals is most easily evaluated by the substitution u = 4 – x?? (a) /…

A:

Q: Determine the lengin or he cuive x* y = 4 1 1<x< 2 8x2, by completing the calculation of the…

A:

Q: Evaluate the integral |x'(x* – 7)6 dx, by making the substitution u = x* – 7. +C Note: Your answer…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. 2x V…

A:

Q: Evaluate the integral J 2x(x² + 6)¨ dx using the substitution u = x2 + 6. | 20 (a? + 6) " d.x +C

A:

Q: Choose the most appropriate answer: +0o 18 dx Evaluate the integral : J, 1 o -9 10 O 18

A: To find: ∫1∞18x3dx

Q: Determine the following indefinite integral.

A:

Q: Evaluate the following integrals Sa 4 |(x? + 4vz - - 6)dx x3

A: To solve integration of such type. You just need to integrate individual terms separated by either +…

Q: Use the value of the first integral I to evaluate the two given integrals.

A:

Q: 28 t2 sin 2t dt

A:

Q: Evaluate the definite integral.

A: Now consider,

Q: Which of the following integrals is equal to the integral (3x-s) dr? 7/3 A |dz 713 B D

A: Please see the answer below.

Q: Consider two integrals: (b) S, x³dx Where a, B> 0 are both positive real numbers. Given that a < B,…

A: In the question we have to determine which integral is larger.

Q: Evaluate the definite integral. '4 I 4? + 2)°x dx

A: Let x2+2→u Differentiating both sides of the above equation with respect to x, we get…

Q: rect answer to evaluate the following integral dx 1 I (1 – x4)Z

A:

Q: Evaluate the integral by making the given substitution. x³(10 + x*)7 dx, u = 10 + x4

A:

Q: Evaluate the definite integral. 5x /2 2ecos ( z) sin(z)dz

A: We need to evaluate the following integral I = ∫05π22ecosxsinxdx…

Q: Use the substitution formula to evaluate the integral. dx 1. 22 11 11 O00

A: Solving the problem by substitute method.

Q: 12-1 – 1|r dr 1|x dx

A:

Q: Evaluate the given integrals. 4. J(secx + tanх)? dx

A: Given problem:- ∫ (tan(x) +sec(x))2 dx

Q: The value of the definite integral csc adx is 0 1 -1 1/2

A:

Q: Choose the most appropriate answer: Evaluate the integral : J 3x2 dx x3+20 O In(x³ + 20) + C T 40) -…

A:

Q: Express the integral in terms of the variable u, but do not evaluate it. e14 In x dx; u = In x e…

A: Express the integral in terms of the variable u.

Q: x? dx (x² – 25)5/2

A:

Q: Evaluate the given indefinite integral. Indicate u, n, and du. [5lan2P etan 28 sec² 2 Bd ß

A: Let I=∫5tan2βetan2βsec22β dβ

Q: Evaluate the integral. 4 – e2× dx = +C

A:

Q: Evaluate the definite integrals 36 a) Vi dt = ... ... 16 b) dz 3D ... ... 64 c) 返 dx = %3D

A:

Q: Evaluate the f 2 3 8xy dxdy=? e following integral by usin tes -8 dA = ?

A: We have to find the value of the given integration according to the given information

Q: Use the substitution formula to evaluate the integral. , π/2 20) cot x csco x dx T/6

A: on solving this we get

Q: Evaluate using the Reimann Integral: S (a2 + 5) dæ 128 3 100 3 128 None of the choices. Please refer…

A:

Q: Evaluate the integral 50 3)dx - by making the substitution u = x 6 – 3. + C NOTE: Your answer should…

A: We will integrate the following.

Q: Evaluate the definite integral. ∫1/6 1/2  Csc  πt Cot  πt dt

A: Evaluate the definite integral. ∫1/6 1/2  Csc  πt Cot  πt dt

Q: Determine the following definite integrals: 3 (c) / 12x – x²| dx (a) [a- | (1+ v25 – x²) dx…

A: Evaluate the integrals:

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫e2t cos 3t dt

A: Given, ∫e2tcos(3t)dt

Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

A:

Q: Use the substitution formula to evaluate the integral. T/20 (1.clan 5x) sec2 5x dx Select one: O A -…

A: Substitute the trigonometric function in some other variables.

Q: Evaluate the integral (exact value). e6sin (87) + C e6x sin(8x) dx 7

A: We can find the integral as below using integration by parts as below.

Q: esin(e")dx 8 cos (e*

A: Evaluate: ∫exsinexdx8cos2ex

Q: Evaluate the integral. T/6 | 9 sec'x dx 2. п/6 |9 sec?x dx = 3/3 (Type an exact answer.)

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.