17. Evaluate the indefinite integrals. a) sin x cos x dx x +4 b) S dx (x2 + 8x- 7)2 c) S sin x dx COs x

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

A:

Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: For the integral x cos. X cosx dx

A:

Q: Find the integral of x^2 * cos(4x) dx.

A: To compute the indefinite integral.

Q: Evaluate the integral: integral from 0 to Pi/2 of cos^3(x)*sin^(2/3)(x)dx

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Q: Evaluate the integrals

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Q: Evaluate the integral.  integral  sec  x  tan  4 x  dx

A:

Q: 7. Evaluate the integral using integration by parts. S cos (5x)e 2* dx.

A: Given the integrationI=∫cos(5x)e2xdx

Q: Evaluate the integral.  integral  sec 3 x  tan  4 x  dx

A: Given

Q: Use integration by parts to evaluate the integral: sin(In(9x))dx 1 x(sin (In)(9æ))– cos(In (9x)) + C…

A:

Q: dx 2+2 sinx + cos x

A: Given that the integral ∫dx2+2sinx+cosx. Evaluate the given integral. Formulae used:…

Q: 1 use this fact and the properties of integrals to evaluate dx =3 (7 – 6x2) dx. Given that

A:

Q: Evaluate the integral: CT/2 cos² (4x) sin³ (4x) dx.

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Q: 7) Evaluate the integrals a) 3(x + 1)²dx b) secx (tanx +cosx )dx

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

Q: Evaluate the integrals. ∫sin 2x/(1 + cos2 x)dx(Hint: sin 2x = 2 sin x cos x.)

A: We have to evaluate ∫sin2x1+cos2xdx We know that sin2x=2sinxcosx So, the given integral can be…

Q: Find the f' (x) 1. f(x) = In( tan2x) 2. f(x) = sin x/ 1+sin x Evaluate the integrals 1.…

A: Our Aim is to find f'(x) where f(x) is given below:-(1) f(x)=ln (tan2 x)Solution⇒Since, f(x)=ln…

Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

A:

Q: Evaluate the Integrals:  a) ∫0π/2 cos5 xdx b) ∫ e2x sinx dx

A: Consider the given information: To evaluate the integrals

Q: Evaluate the integral.  integral  sec 5 x  tan  4 x  dx

A: Integration:                    ∫sec5(x)tan4(x)dx                    Solving using Trigonometric…

Q: 3. Evaluate the integrals √tanh x sech² xdx

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Q: Use any method to evaluate the integrals ∫x cos3 x dx

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Q: Evaluate the integral. integral 0  to pie /2     sin 3x  cos 2x dx

A: Consider,

Q: x cos x-sin x Jr dx x²

A:

Q: Find the indefinite integral. S-x² + sin x – 3* dx | In |x| – - 3* + C COS X - 3 In 3

A: detailed solution is given below

Q: Find the indefinite integral using integration by parts with the given choices of u and dv. |x…

A:

Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

Q: set up an integral ....bounds x=3pi/4 x=-pi/4 y=-sinx and y=-cosx

A: GRAPH

Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

A:

Q: Evaluate the integral.  integral  (1- sinx )/ cos x  dx

A: ∫1-sinxcosx dx

Q: Evaluate the integral.  integral  sec3  x  tan  4 x  dx

A:

Q: Evaluate the integral

A: The integral is given by,

Q: Identify which among the numbers are odd-numbered integrals. 1. S21 cos 7x dx 2. S csc* dx 14. S dy…

A:

Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: find the indefinate integral of sin^5(x)cos(x) dx

A: I = ∫ Sin5x  Cos x dxLet Sin x = tCos x dx = dt

Q: Evaluate the integral/ cos'x sin x dx using the substitution u = cos x. cos"x sin x dx =

A: ∫cos11xsinxdx

Q: Evaluate the integrals

A:

Q: Evaluate the integral. integral 0  to pie /2    cos x + sin x dx

A:

Q: Compute the indefinate integral. integral (1-sin^2(x))/cosx * dx

A: Consider the given integral.

Q: Evaluate the integrals ∫cos x cos 7x dx

A: To integrate: ∫cosxcos7xdx.  We know that cosacosb=12sina+b-sina-b. Therefore, using the above…

Q: Compute the indefinite integral 2. 4e2a + 6x 5) dx. - -

A:

Q: Evaluate the integrals ∫cos 3x cos 4x dx

A: Evaluate ∫ cos 3xcos 4xdx

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

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Q: Evaluate the integrals in 1 1. Vx(1 + x) sin x sec x dx

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Q: Evaluate the integral. ∫x  Cos2 x dx

A: Given- ∫xcos2x dx To Find- The value of the above integral. Identity Used- cos2x=1+cos2x2

Q: In x dx

A: Given: ∫lnxx2dx Integrate the given integral using the integration by parts formula.

Q: Evaluate the integral. (Use C for the constant of integration.) cos(x) (4 + 8 sin²(x)) dx

A: Solve the intregal

Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

A:

Q: Evaluate the integrals ∫8 sin4 y cos2 y dy

A: the given integral is: ∫8 sin4y cos2y dy we have to evaluate the given integral.   let the given…