Evaluate the following definite integrals, a. t(1-t)2 dt = V312 dr b. VI- C. 12x-1|dx=

Q: Find the following definite integrals. (a) Sx³V2+x² dx (b) Sx² In x dx (c) S3e-2* sin x dx

A: Use Integration by parts and substitutions method

Q: Find the following integral: S- -4 /x² dx x3

A: Explained below

Q: Evaluate the following definite integrals: а. бх dx (4 – x2)*2

A: topic - definite integral  note : as per bartleby guidelines we are supposed to answer only first…

Q: Approximate the following integrals using the Trapezoidal rule. 0.5 [h=24 dx x-4 a. [x² dx 10.5 b.

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Q: ~3 (x/x+1)dx

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Q: Evaluate the following definite integral. 5 dx 2 0 √x + 169

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Q: Evaluate the following definite integral: dx = 12

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Q: 7. Į V1- xdx 8. ſ e2x dx

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Q: Evaluate the following integrals: a. | Vē sin(2t3/2) dt

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Q: [ (2x+6)*dx 3.

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Q: 4. dx (x² +1)*

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Q: d) V1+x? dx

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

Q: 1 dx 1 -3

A: see below the calculation

Q: dx

A:

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: x² So (1+x6) ³ dx

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Q: 4x dx 1+ x²

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Q: Evaluate the following definite integrals.

A: Given1.∫03xx+1dx2.∫01x(3+x)5dx

Q: Find the indefinite integrals: x5/2 + 4x + 1 dx a) / ? b) / (a" 6t7 2 + Te' ) dt t3

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Q: S x² √x²+4 dx

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Q: Differentiate each of the following definite integrals. d а. dx J2 * sin(t )dt 24 d с. dx i San(e)…

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Q: T6 Based on the image attached, differentiate each of the following integrals with respect to x.

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Q: Find the following indefinite integrals. X dx= Vx6 +C

A: Given,

Q: Vex – 1 dx c2

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Q: 1 dx

A: Topic:- integration

Q: Evaluate the definite integral from 0 to 1 of dt/sqr(t^2-6t+13)

A: Given integral is

Q: 00 dx 1 3 x³ (x²-9)Z x2.

A: Let I is the value of given Integral.

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: Q3 Evaluate the following integrals X. cosh? () dx -In2 1 - | 2 - cosh(lnx) dx

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Q: Q1 - Evaluate the following integrals i. " xe-*dx

A: We are evaluating the following integral:

Q: Evaluate the given definite integral, if it exist. V4 + 3x dx

A: Given that finite integration and we find its value by using integration formulas. We know that…

Q: Find the indefinite integral. | Vi (e* +t - 1) dt

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Q: 4 2 - VE dt t2 1

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: Find the following indefinite integrals. dx = (m) / (~- (bị + 3e" + dt =

A: (a) I1 =∫x3-1xdx (b) I2=∫eπ+3e2t+1etdt We know that  ∫xndx=xn+1n+1+c and ∫enxdx=enxn+c

Q: Q2 – Evaluate the following integrals. 1 vi. S7 dx (sinhx+coshx)2

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Q: 6 sec*x dx

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Q: Find the exact value of the definite integral below, using the substitution u = x x (√6+√2) 1+x² -…

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Q: Evaluate the following integral. 1 dx /x + 4

A: By using integration formula, we calculate the given integral.

Q: dx x V1-4 In²x

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Q: find formulas for the functions represented by the integrals.

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Q: Find the following definite Integrals : Wir ( i+ sec?x)dx 2. a. X.

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Q: 4/3 /3) dx -1

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Q: Evaluate the following indefinite integrals. 1. Jx²dx 2. S(x³ + 2x)dx 3. S(a)dt :a = constant

A: Solving the problem by finding the indefinite integral.

Q: Evaluate the definite integrals a) Vi dt = 16 1 dz = b) 64 / dx = 8.

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Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: Evaluate the following integrals.

A: ∫x91-x20dx=∫x91-x102dx Now put, x10=t⇒10x9=dtdx⇒x9 dx=dt10

Q: 1 1 x=6 x - 2 dx +oo

A:

Q: Evaluate the following definite integrals. (а) |2t – 4| dt. /- (b) cos(3x) dx. (c) d.x.

A: You must have an idea about definite integral to solve these questions. In these types of integral…

Q: Evaluate the following integral 1 dx (x – 5)²(x + 3) a

A: We have to evaluate the given integral    The given integral is   ∫1(x-5)2(x+3)dx