Evaluate the definite integral. dx x(1+ In æ)

Q: evaluate the definite integral.

A: We rewrite the given integral using the double angle formula

Q: Evaluate the definite integral. (Assume a > 0.) 'al/5 x°Va? - x10 dx

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

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Q: Evaluate the following definite integral: dx = 12

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Q: Evaluate the definite integral. e4 dx xylnx

A: We can evaluate the integral as below.

Q: dx 1 sin xcot;x

A: We need to evaluate the indefinite integral ∫dxsin12x cot12x Now, we will use the fact that cot…

Q: Evaluate the definite integrals. 7/4 a) z tan(x?) dx b) [ 5a*e dx

A: (a) ∫0π/4xtanx2dx Let, u=x2 The derivative of the above equation. dx=du2x The lower limit is, a=02=0…

Q: Evaluate the definite integral. (Assume a > 0.) 'a²/5 x*Va? - x5 dx

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Q: Evaluate the following indefinite integral. Do not include +C in the answer. 3 dx

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Q: Evaluate the definite integral. e !/x5 dx 1 to

A: We have to solve integration by put  1/x⁵ = t

Q: 71. Perform the following definite integral. 2 |(1-e-/2) dx = x=0

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Q: 23 dx 'e xyIn x

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Q: dx

A:

Q: Evaluate the definite integral.

A: Consider the given integral. I=∫-π3π3x4sinx The given function is continuous function in the given…

Q: Зу? + у — 1 y?

A: We have to solve the given definite integral: ∫123y2+y-1y2dy Rewriting the integral and solving the…

Q: Evaluate the definite integral: T/6 sin8 cos e de

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Q: dx I = е. a² +x²

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Q: sin(In.x) a.

A: Take substitution lnx=t.

Q: А A = e sin xda

A:

Q: Evaluate the definite integral.

A: Given:∫sin2x dxFormula:sin2x=1-cos2x2

Q: Evaluate the following definite integral : 8. 1 + X dx X

A: Given,          ∫08x1+xdx

Q: dx The integral can be rewritten as 1- x

A:

Q: Evaluate the definite integral. 2 e 1/x5 dx х5

A: The given definite integral is,

Q: Evaluate the definite integral. 1/2 + a? dx (a > 0)

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Q: b) Calculate the following definite integral: [*(√x - 3) dx

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Q: Evaluate the following indefinite integral. 3 dx +C

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Q: dx The integral can be rewritten as 1-x

A: Given that the integral  ∫-∞0dx1-x We can write this integral  limx→-∞∫s0dx1-x

Q: Evaluate the following definite integral. 1 83* dx = %3D

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Q: /2+In x dx

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Q: Evaluate the following definite integral. a) 3 dx 2x +

A: Given: a  ∫142x+3xdxb  ∫π/3π/2sec2x2dxc ∫01e1-xdx

Q: Compute the definite integral. ? 0 6ex sin(x) dx

A:

Q: Evaluate the definite integral. dx .2 X* + 19 0.

A: Given: The definite integral∫09xx2+19dx To find the value of the given integral. Use the…

Q: /3+ |æ| dx -3

A: Given integral, ∫-333+xdx

Q: e +1 dz e + z

A:

Q: Evaluate the definite integral xp, a) S b) S

A: ∫011+7x3 dx Consider, ∫1+7x3 dx=∫1+7x13 dx=1+7x13+113+17+C     ∵∫xn dx=xn+1n+1+C & x-coefficient…

Q: Evaluate the definite integral. esin (a) cos(x) d x

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Q: Evaluate the definite integral. 'al/3 x5, х6 + а? dx (a > 0)

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Q: Evaluate the definite integral. e4 – x dx 14

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Q: Find the indefinite integral

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Q: Evaluate the definite integrals. (a) ſ°, 2r(x² – 3)³ dx

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Q: Evaluate the definite integral. e2 - x dx

A: The given integral is as follows. Let u=2-x. Then, du=-dx. The Lower limit will be u=2-2=0 and the…

Q: Evaluate the definite integrals a. help (numbers) b. 6e dx

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Q: b) Evaluate the integral x? e* dx.

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Q: Evaluate the definite integral: 1 dx 2. x· COS

A: Solution

Q: Evaluate the definite integral. e 1/x dx

A: Now consider,

Q: Evaluate the definite integral. "Tt/2 " d(sin x)? dx = (sin x)2 dx =

A:

Q: Evaluate the definite integral. e + 6 dz e? + 6z

A: We need to evaluate the following limit ∫01ez+6ez+6zdz                             .........1

Q: evaluate the given integral.

A: To evaluate the integral: ∫ x2e-xdx Formula used: Integration by parts: ∫uvdx=u∫vdx-∫dudx·∫vdxdx

Q: Evaluate the definite integral (assume a> e. 49

A: Given integration is : ∫0a29x8a2-x9dx To find the value of integration