Evaluate each definite integral. 1) - 4x² + 6) dx

Q: Evaluate the integral.

A:

Q: 1. Evaluate each integral using "u" substitution. 12x(3x2 – 1)* dx A. - x*csc? (x³) dx В.

A: evaluate the given integral  A. ∫12x3x2-14 dxB.∫-x4 csc2x5dxsolve it by using u substitution

Q: Evaluate the integral. Зл /2 7|sin æ| dæ

A: Consider the given integral

Q: 12) Find each integral by substitution xe

A:

Q: 52? + 3х — 2 dx. x3 + 2x2

A:

Q: Evaluate the definite integral. ra?/3 xVx6 + a2 dx (a > 0)

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Q: a + 3 da r2 + 10a + 74 е.

A: since you have ask multiple questions , so we will answering only first question.

Q: VI 3xdx 4 + x

A:

Q: 1. Evaluate each definite integral us 2 (a) 4r? dz -1

A: We have to solve the following given definite integral

Q: Evaluate each definite integral 4. L-5 (x + 2)šdx

A: To solve the given integral :- First put t=x+2

Q: Evaluate the definite integral

A: Given,

Q: Evaluate the given integral. [ 2x?sin(4x)dx

A: The given problem is solved below in detail.

Q: Evaluate the integral. n/2 5 cos?0 de

A:

Q: Evaluate the integral: So " (10 + 2z? + 2y²)dx dy. 160 3. 100 3. 110 3. None of these. 140 3

A:

Q: Solve the following improper integral : x3 + x? x6 +1 8

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Q: Use the substitution formula to evaluate the integral. 3 coe? x sin x dx /3 129 1024 O 21

A: From the given problem: I=∫π32π3cos2xsinxdx    ...1 Using the substitution method to find the…

Q: Evaluate the definite integral 9. (10х + 3)da 3.

A: Given, The definite integral  ∫3910x+3dx  We have to evaluate it.

Q: Evaluate the indefinite integral.

A: Integrand = 6x3(8 – x4)2 = 6x3(64 – 16x4 + x8) = 384x3 – 96x7 + 6x11Hence, the given integration is…

Q: Evaluate the integrals.

A:

Q: 12) Find each integral by substitution a) [xe dx -dx- b) 7+9

A:

Q: Evaluate the definite integral (12x? – 2x + 3)dx

A:

Q: Evaluate the integral | tan?x sect x dx

A: Given : ∫tan2x sec4x dx

Q: Evaluate the Integral.

A:

Q: Evaluate the definite integral.

A: Given: I=∫oaxx2+a2dx          , a>0 for evaluating given integral, we substitute x2+a2=t2…

Q: 2 re' dr c.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 8) dx 7)

A:

Q: -In 2 In2 1(e* – e¯*) dx In 22

A: Let I is the value of given Integral

Q: 了 /2 csc x cot xdx /4 26.

A: From the given problem:   I=∫π4π2 cscxcotxdx   From the standard form of integration.…

Q: Evaluate iterated integral.

A: Given, I=∫16∫1615xydxdy

Q: 3lnx² -dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3x e - е dx 3x e*:

A: The given integration, ∫e3x-e-xe3xdx

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: Find or evaluate the integral by completing the square.

A: Given that, ∫021x2-2x+2dx

Q: Evaluate the definite integral. Fcos (x6) dx

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Q: I just need help solving this integral

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Q: 6. [t cos"(7*) dr

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Q: Find the value of n in the following definite integral. 4x° dx = 1 Answer:

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Q: Evaluat each Integral. For definite integrals, give exa Only, S X (2-5x)*dx dt

A: Topic:- definite integration

Q: 1+ 9cos5 (8w) dw 27. sin? (8w)

A: Part 27,

Q: Evaluate the definite integral | (12a? – 10x + 9)dx

A:

Q: 3. Evaluate each definite integral by using geometric formulas. (a) 14.x – 12| dr dr (b)

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Q: Find an expression in a and b for the value of the definite integral: ∫ba [2x2 + √x + 5]dx

A: Evaluating the definite integral

Q: Evaluate each integral. d) ſe* sin(9x)dr

A: We have to evaluate, ∫e3x sin(9x) dx

Q: (15x? +10)*(30x)dx

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Q: dx (6-х?)3/2

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Q: | Evaluate the definite integral: 4+ 5x? dx

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Q: Evaluate the following integral.

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Q: Evaluate each definite integral -14 1. Ldx -4 r4 (x2 2. — х — 2 dx 2 2

A:

Q: Solve the following integrals through video presentation. 12x + 6 1. =dx √x² + x

A:

Q: 3) Find each integral by substitution 2x+1

A: Given, ∫12x+1dx  we have to solve given integral by subsititution method

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.