3. Calculate the integral dz, (ke R), and use it to calculate the value of the integral cos(k sin0)d0.

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Q: Compute the following integrals. 1 (i) Ss(0.2) sin*(e) cos(2) dz.

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Q: |(x² + 2x) cos(2x) dx

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Q: Find the value of the following integral: * COS2 dx,a>0

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Q: Evaluate the following double integral (x² cos y – sin x)dxdy. 0.

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Q: To evaluate x² /1-x² dx using trigonometric substitution, what is the new integral in terms of 0 ? A…

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Q: Can i get help step by step

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Q: Calculate the integral of 6 (cos 30) d0.

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Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: Consider the following integral: dx I : a. Use the substitution u = x - 1 to show that I = sin(2x –…

A: Indefinite Integration

Q: has the form - F(0)+ + C: What should be the value of e to make F(o)=0? The resulting integral of…

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Q: The given integral (cos?r – sin²x) dx is equal to

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Q: ·S- The integral x dx x²+√√√x²-1-1 can be transformed to which of the following using trigonometric…

A:

Q: evaluate the integral.

A: Let the given integral as

Q: Consider the following integral dx After making the trigonometric substitution r = 3 sin 0, which…

A: From the given problem:   I=∫dxx29-x2 ...(1)   Now, substitute in equation(1).…

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Q: Solve the following Integral Equation: r"()= cos(r)+ [x^(x}sin(t – x\k&x. (0) = y'(0)=0

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Q: Evaluate the following double integral (x², coS y – sin x)dxdy.

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Q: 1/3 13 sin t dt cos? t

A: Find the given integral

Q: O Find the inde frinite in tgal 曲 A cos (2¢) df

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Q: 1+e² sin z + z cos z

A: Introduction :

Q: Find the indicated integrals. In(25) dæ =+C (a) e cos(e') (b) 2 + 6 sin(e') dt =+C 5/6 sin '() (c)…

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Q: Find the integral. e4X cos 3x dx + C

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Q: Evaluate the given integral. ∫ (e2x cos x -2e2x sin x)dx.

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Q: Consider the following integral (r+ 2)²dx J V5 – 4x – x² After making the trigonometric substitution…

A:

Q: T/2 COS z xp V4 - sin? a

A: givenI=∫0π2cosx4-sin2xdxsubstitute  sinx=t therefore limits will change t=sinπ2=1  to t=sin0=0after…

Q: Evaluate the integral. -1/4 S" 5 sin* 2nx dx

A: here we us the sine reduction formula to solve the given problem ∫(sinnx) dx=-cos(x)(sin…

Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: Evaluate the integral COS nx dx

A: To solve the integral we use integral by parts formula. From integral by parts formula we get: ∫uv…

Q: Q1)Evaluate the following integral: Sz cos . sin dx 2 2

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Q: Evaluate the integral. 1/2 cos(t) dt 1 + sin?(t)

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Q: Evaluate the integral. cos(0) d0 Tt/2

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Q: Evaluate the iterated integral. cos e p2 sin o cos o dp dê dọ rT/2 1/4

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Q: Find the indefinite integral.∫(cos5 t/√sin t)  dt

A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

Q: Evaluate the iterated integral. * T/6 cos(e) 7r5 sin(8) dr d0

A: Explanation of the answer is as follows

Q: Evaluate the iterated integral. cos(e) 3r2 sin(e) dr de

A: Given query is to find the value of the integral.

Q: Find the value of the following integral: cos2r dx,a>0 71+a

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Q: Calculate the following integral: (cos(x)) ·(e***) dx

A: The given integral is, ∫cosx·e4xdx. Let I=∫cosx·e4xdx Use integration by parts and solve the given…

Q: 1. Evaluate the following integrals. sc 8)(1+ sin² 0 + sin 0 cot? 0) d0 a.

A: Given: I=∫cscθ1+sin2θ+sinθcot2θdθ     Use the trigonometric identity; 1). sinx=1cscx 2).…

Q: Evaluate the integral. 7/2 cos(t) dt V1+ sin?(t)

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Q: Evaluate the integral. cos(0) d0 π/2

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Q: dr Solve the given differential euation: + rtan 0 = 7cos0. de %3D r = (70 + C') cot0 Or = (70 + C)…

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Q: 1 To evaluate the integral dx, using a trigonometric substitution, which x2 + 6x + 13 substitution…

A: Make the denominator in standard form than do the substitution such that integration become simpler.

Q: By the even extension method applied to the function f(x)= e-16z, where a > 0, the value of the…

A: The given function is, f(x)=e-16x,x>0

Q: Evaluate the definite integral. ra/2 cos(t) dt 13 + sin(t) 0/

A: We have to solve the integration

Q: Evaluate the iterated integral. cos(e) 7r° sin(0) dr de /3

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Q: Evaluate the following integral. T/6 T VI+ cos(6t) dt

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Q: 27n 4 cos x sin x dx 7/3

A: