The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y y = f(x) 2 4 6. 8 (a) f(x) dx '5 (b) f(x) dx (c) f(x) dx 6. (d) f(x) dx

Q: Evaluate the integral. (Use C for the constant of integration.) | (x2 - x) dx

A: We can solve the indefinite integration.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) Jx x5/2 In(x) dx

A:

Q: (c) Evaluate * sec x tan x dx using the table of standard integrals.

A: a) i) It is required to find ddxetanx. Differentiate etanx with respect to x. ddxetanx=etanxddxtanx…

Q: Evaluate the integral. (Use C for the constant of integration.) 13 tan (x) sec (x) dx

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral   [ 2x 3  - 3…

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Q: Evaluate the integral. integral    (  x 2 -x +6  )/ (x 3 + 3x) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) cos(x) dx

A: ∫tan8xcos9xdx

Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) tan(x) cos(x) dx

A: ∫tan8xcos9xdx

Q: Evaluate the integral. (Use C for the constant of integration.) 10e-0.7x dx

A:

Q: r" (tan (x)) (In (cos(x))) dx

A: solve this integration by substitution. substitue                    ln(cos(x)) = t on solving

Q: 5e5x dx

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Q: Use a table of integrals to find the indefinite integral

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Q: Use the tabular method to find the indefinite integral. ∫(1 − x)(e−x + 1) dx

A: We multiply the integrand then integrate each part…

Q: x e* dx (1+х)2

A: Explanation of the answer is as follows

Q: Evaluate the integral. (Use C for the constant of integration.) 7 arctan(x) dx

A:

Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: Evaluate the integral. (Use C for the constant of integration.) | tan (x) cos°(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 4 tan(x) sec (x) dx

A: Given the integral, ∫4tan(x)sec3(x) dx = I(Say) Now, I=∫4tan(x)Sec(x)sec2(x) dx.........(1)  Now…

Q: Find the integral of (x)(arctan x) dx,

A: Given: evaluate

Q: Evaluate the definiteIntegral. integral 1/2 to 1 cosx^-2/x^3 dx

A: The given integral is ∫121cosx-2x3dx. Let u=x-2. Then, du=-2x-3. The lower limit will become…

Q: Evaluate the integral. (Use C for the constant of integration.) (arctan(x))5 | x2 + 1 dx

A:

Q: a) Use Trapezoidal and Simpson's Rule to evaluate the integral , (2x – 1)dx by taking n=4

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (tan²(x) tan^(x) dx

A: Given       I=∫7tan2x++tan4xdx      = 7∫tan2x1+tan2xdx      = 7∫tan2x.sec2x dx∵sec2x-tan2x=1

Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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Q: Evaluate the integral. (Use C for the constant of integration.) 9x dx

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Q: Use a table of integrals to find the indefinite integral ∫√x arctan x3/2 dx

A: The given integral is I=∫xtan-1x32dx. Concept used: By part of integration ∫udv=uv-∫vdu Calculation:…

Q: Evaluate the integral. (Use C for the constant of integration.) x²e&x3 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) ln(√x) dx

A: I = ∫ln(x)dxUsing,     ln ab=b ln aI  = ∫ln(x)12dxI =12∫ln(x) dx

Q: Evaluate the integral. (Use C for the constant of integration.) 1- sin(x) dx

A:

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral     e x  / (3…

A: We have to evaluate the integral: ∫ex3-e2xdx Rearranging the given integral, ∫ex3-ex2dx In this case…

Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) cos7(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) (ln(x))2 dx

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Q: Evaluate the integral using integration by parts where possible. (Use C for the constant of | (x2 -…

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Q: Evaluate x dx from the definition of RS-integral.

A:

Q: Evaluate the indefinite integral dx: %3D

A: topic - indefinite integral

Q: dx is: value of the integral sinx the Using Simpson's rule 113,

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 2 tan3(x) sec(x) dx

A: Let sec(x)=t sec(x)tan(x)dx=dt tan2(x)=sec2(x)-1 Substituting we get 2 int (t2-1)dt =2 (t3-t)+C…

Q: Evaluate the integral.   ∫0√3 arctan(1/x) dx

A: Given:∫03 tan-11x dx

Q: Determine the value of the integral: integral sign:  (x^2)(e^-x^3)

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Q: Evaluate the integral. (Use C for the constant of integration.) | 2000e0.1x dx

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Q: Evaluate the integral dx et – e-x Note: Use an upper-case "C" for the constant of integration.

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Q: Use a table of integrals to find the indefinite integral ∫x arccsc(x2 + 1) dx

A: Consider the given integration as ∫xcsc-1x2+1dx

Q: Evaluate the integral. (Use C for the constant of integration.) dx 5x(1 +5x)

A: Evaluate the integral using trigonometric substitution

Q: Evaluate the integral using Integration by Parts. x-e* dx Use C for the arbitrary constant. x²e* dx…

A: Topic:- application of integration

Q: Evaluate the integral. (Use C for the constant of integration.) ∫ 3 tan2(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 tan(x)sec^3(x)dx

A:

Q: Evaluate the integral | 2 cos(In(x)) dx, x > 0 Note: Use an upper-case "C" for the constant of…

A: Given information: The integral is ∫ 2coslnxdx. Concept used: Integration by parts: ∫udv=uv-∫vdu…

Q: sin'(x) cos(x) dx

A: