Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x + y)j along the path consisting of a line from (n, 0) to (2, 5) followed by a line to (7, 0) followed by a quarter orde ta Rubmil o

Q: 3. 4r sin(4r + 5) dr ( 4x10 + 2xª + 15.r" 4 + (3r r² + 1 – 5)") 4. dr

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Q: Use u-substitution to find the definite integral |4xe -3x+7 dx . Please clearly show all -k.

A: By u - substitutions

Q: Evaluate the iterated integral ¡¡ -1 -2 (17x+8y + 10) dx dy.

A: I=∫−10∫−22(17x+8y+10)dxdy

Q: 41. | sin &r cos 5x dr

A: This integral can be done by using the trigonometric formula In the given question a=8x and b=5x…

Q: Find the integral of ∫(sin2x - cos2x)2dx. Use trigonometric transformation or integration by parts.

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Q: 6 2" – 5 sin(r) + dx 1+x?

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Q: Integral: Evaluate -2 sin 2x xp= V9+ cos² 2x

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Q: Exerceise (6) Prove that Jy2 = 2 sinx

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Q: 6z* cos (r*) dr-

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Q: Find the integral of sinx dx x – 7 8.

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Q: 1 2 (x+1)² dx

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Q: rt01+sin x +00 -dx x2

A: Here we will use  integration by parts  ∫uv dx= u ∫v dx -∫dudx∫vdxdx

Q: Exercise(6) Prove that J1/2 = XT sinx 2.

A: Here we have to prove that  J12=2xπsinx

Q: Find the integral. cos'xsin²x dx a. sin³x-sin5x+C O b._sin³x+sin5x + C Oc_sin x + sin³x + C с. O O…

A: We have to integrate (cos3x)(sin2x) w.r.t x

Q: 8. Evaluate the integral 4 + 6x dx Vx

A: In this question we have to solve the integration given. we can write , x=(x)12

Q: 2 8 dx 1 x(x²+2)² 3.

A: Solve the following integral

Q: 6x + 8 + 8x)2

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Q: Set up - simplify a little bit, but do not evaluate y = sin x- I cos z for 0 < x <T/2. the integral…

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