Which of the following is the general power formula for integrals whenever n # -1? Sx"dx = x"+1 + C S x"dx = + C n+1 Option 1 Option 2 Sx"dx = + C S x"dx = - + C

Q: Evaluate the integral. 6. 6 cosh (x) dx X, 4

A: Let x=u Differentiating both sides with respect to 'x', we get ddxx=ddxu12x=dudxdxx=2du

Q: Compute these integrals: dz 3114

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: 5. Determine if the integral is conve 0. exdx -1/2 V1-e 2x

A: Given query is to find integral converges or diverges.

Q: 2 B. Evaluate | (2- x) dx by interpreting the integral in terms of area. -1

A: Topic = Integration

Q: Evaluate the integral of xydx from x =3 to x=6 when x = 6cos angle and y=2cos angle

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Q: Suppose if 0 < x < 4, (12 – 3x | 3x – 12 f(x) : if 4 < x < 8. Evaluate the definite integral by…

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Q: Determine the integrals of the followings: (i) S(3x2 + 5x/2 +- )dx (ii) (20 + sec? x) dx 10 20 +…

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Q: Evaluate the integral: Integral with bounds of 2 and -2 ez/2/ez/2+1 * dz

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Q: Find the indefinite integral z/4+z'dz.

A: Given : ∫z24 + z3dz

Q: Suppose further that a <c<b. Which of the following is a property of an integral?

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Q: Find the indefinite integral.

A: Given data: The given expression for the integration is: .   Assume (z-10)=t  and differentiate it…

Q: Calculate the indefinite integral: ∫ (9t−2/3 + 4t7/3) dt

A: Integration formulas help to find the integration of the given function. The integration formula…

Q: Calculate the integral, assuming that f(x) dx = 8 and g(x) dx = 3. (Give your answer as a whole or…

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Q: Calculate the integral, assuming that 6 f(x) dx = -3 and 6 g(x) dx = 20. (Give your answer as a…

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Q: Use the properties of integrals to evaluate integral 0 to 1 (4+3x2 ) dx

A: Given: I=∫014+3x2dx for evaluating given integral, first we separate terms then integrate it

Q: Evaluate Integrals 1 √ ₁ (2 + √5) √5 dy

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Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

Q: Se (壁 0,6 + 100X1 2,943 100X1- 0,6 0,9 r0,36+

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Q: S sec?(5x+8) dx=?

A: The objective is to evaluate the integral.

Q: Sy+ –3-dy у (3–2) 3

A: Our Aim is to find the integral of ∫y+3(3-2)23dy -(i)

Q: Find the indefinite integral. ap- -&x +9 In] –&r² +9| + C a. -&r+9 b. Inl -&r +9|+C c. In| -&r +9|+c…

A: We need to evaluate the following integral I = ∫x-8x2+9dx                                .......(1)

Q: Calculate the integral, assuming that 6 f(x) dx = -2 and g(x) dx = 37. (Give your answer as a whole…

A: Solve the integration

Q: Use the Table of Integrals to evaluate the integral. Show ALL work. S 11x³√4x²x¹ dx

A: Follow the procedure given below.

Q: Evaluate the integrals

A: The given integral is ∫12 s2+ss2.

Q: Which one of the following integrals represents the area between y = x' and y = 12 + 2x for -1 < x <…

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Q: Which of the following indefinite integral has a general antiderivative of: * 5 1 x4 −²x³ + x² − 7x…

A: We know that integration and differentiation are inverse operations.

Q: | 3t°(t° + 2)*/² dt 8. 3/2

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Q: 3 Use only the fact that 3x(4 - x)dx = 22 and the properties of integrals to evaluate the integrals…

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Q: de 1+tan 0 k/2

A: Let I=∫0π2dθ1+tan θ      I=∫0π2dθ1+sin θcos θI=∫0π2cos θ dθcos θ+sin θ     ....(1)Using property…

Q: Which of the following integration expression can be transformed into integral of power (Ju"du). (c…

A: A

Q: Csch (2 cosh´0)d0 Csch20

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Q: Evaluate the indefinite integral. VA + a*dz ,5, + C

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Q: Find the indefinite integral z(3 +z) dz.

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Q: Evaluate the integral. (In(x))² x3 dx

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Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 ○ ₂²(1…

A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: Evaluate the integrals ∫2eθ cosh θ dθ

A: To evaluate  ∫2eθ coshθ dθ

Q: Calculate the integral, assuming that 6 f(x) dx = -7 and 6 g(x) dx = 20. (Give your answer as a…

A: Consider the following integrals: ∫05fxdx=-7∫05gxdx=20

Q: 1. Evaluate (2 – x) dx by drawing a picture and interpreting the integral in terms of areas.

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Q: 5. Evaluate the integrals using appropriate substitution., a. x*/5+x* dx b. f coszdx os-dx 7x2 +…

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Q: evaluate the indefinite integral.

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Q: Calculate the indefinite integral 4dy V4-9y2

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Q: a) Evaluate the integrals using a dx i) S16x2 1+16x?

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Compute the integral by algebraic substitution:  ∫3x^5√16-x^2 dx

A: The given integral is: ∫3x516-x2 dxLet, I=∫3x516-x2 dx⇒I=3∫x516-x2 dx    -1

Q: Find the indefinite integral. S 8x In(3æ)dæ A. +C B. 8 ln(3x) +8x + C C. 8x ln(3x) –- 6x² + C D. 4r²…

A: To evaluate ∫8x ln(3x) dx...(1)

Q: Evaluate the indefinite integral.

A: Consider the provided integral, ∫z21+z33dz Evaluate the indefinite integral.  Apply the substitution…

Q: HEvaluate the integral 3 In

A: Given

Q: Evaluate the integral using appropriate substitution ∫(x^2 +1)/(√(x^3 +3x))dx

A: Given an integral: ∫x2+1x3+3xdx Let, x3+3x=t t=x3+3xdt=3x2+3dxdt=3x2+1dxdt3=x2+1dx Substitute value…

Q: Evaluate the integral * » In 4 coth x dx In 2

A: In this question we have to solve this integral.

Q: evaluate the improper integral from 1 to infinity: 2/[x(x+2)] dx

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Q: 5/(5x+5x^2+x^3)

A: We apply partial decomposition to calculate the integral.