Evaluate the line integral by applying Green's theorem. a) OT b) 00 c) O eπ d) O-T e) 2π f) O None of these. for ² e sin(y) dx + e* cos(y) dy C: (2-3)²+(y-2)² = 16 4

Q: . Use the I function to do the following: (a) find the value of SVxe*dx ,

A: We shall solve first question only as per the answering guidelines.if you want other question to be…

Q: - Evaluate the iterated integral 3xyz dz dy dz.

A: Definition. • In calculus, an iterated integral is the result of applying. integrals to a function…

Q: JO 18.9. Let y denote the boundary of the rectangle whose vertices are -2 – 2i, 2 – 2i, 2+ i and…

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Q: Find the indefinite integral. |cos 2x ein 2* de sin 2x A) 2 +C ein 2x +C B) C) sin 2x e cos2x +C D)…

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Q: 2) Evaluate each integral below: a) cos(x²) x dx c) (2x-1)2 dx

A: In this question we will solve both indefinite integral.

Q: a) sin(x) + cos(r) - √x+dr x+2x³ dx I c)/3-e dx

A: To find : Evaluate the given indefinite integrals.

Q: 2. Use the Fundamental Theorem of Calculus to find: (a) (b) (c) cx³ de fort+3* cos²¹(y) dy. dx d dx…

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Q: 4. Evaluate the iterated integral T, cos(³) dydx. a. (cos 1- 1) b. 1 e. (sin 1- 1) f. 1 (1- cos 1)…

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Q: a.) S (t² – 9) (4 – t²) dt from 2 to 3 b.) fx dx from 1 to 2 c.) f (x² - d.) f sin 0 de from 0 to…

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Q: Evaluate the integral | (curl F) • n dA directly for F= [e23, e" sin y, e² cos sy], S : z = y²(0 Śx…

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Q: 0 T/2 (sin² t cost + √1+ cos(2t)) dt

A: sin2t = 2Sint cost1 + cos2t = 2cos2t1 - cos2t = 2sin2t2cosA cosB = cos((A+B)/2) + cos((A-B)/2