Let A₁ be the set {(x, y): x² + y² ≤ 1} and let A₂ be the set in R2 bounded by the lines y - 2x = 1, y + 3x = 4, and y + 3x = 8. Compute the following integrals by introducing suitable substitutions: -1, y - 2x JS (x + y) dady = A₁ (1-2² - y²) dxdy (b)(

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

A:

Q: Evaluate the integral. (tant 6t dt tan 6t - tan-6 + 1 tan-6t + 36 tan 6t + t + C 18 1 tan 6t + 18…

A:

Q: Without evaluating the integral, show that √ √ 2 ² 4+1 4₂ | 15 | 1/2 dz where C is the line segment…

A:

Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: x* + x2 + 4 dx. x5 + 8x3 + 16x

A:

Q: Let C₁ be a straight line in the Argand plane from (0, 0) to (3, 3), and let C₂ be the path…

A: We have to calculate the following integrals i∫C1z2dz  and ii∫C2z2dz where C1 and C2 are given…

Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx-2xcosx-2sinx + C C…

A: integration

Q: (4x +3)dx Solve the integral: eln(2x²+ 3x- 4)³ eln(2x? + 3x- 4) A (2x2 + 3x – 4) + C (2x² + 3x+4)* +…

A: