1. Use Green's theorem in order to compute the line integral $ (3cos + 6y?) dx + (sin(5") + 16x³) dy CO x where C is the boundary of the square [0, 1] × [0, 1] traversed in the counterclockwise way.

Q: 3. Evaluate f 2 arctan (2) dx + ln(x² + y²)dy where C is defined by x = 4 + 2 cos 0 and y = 4 sin 0.

A: Let   and…

Q: (1) Evaluate or determine the definite integral: •5п a) | sint|dt, b) ₁dt, c) fe-tdt.

A:

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

A:

Q: Evalúe la integral doble. SIp xcos(y)dA, D está acotada por x = 0, y = x² y x = 1 O -(cos(1) + 1) ㅇ…

A:

Q: 2. Find the following Integrals a) ſe (lnx)³/2dx 1 X 1 -1 tan-¹(x) dx 1+x² c) ſ sin³(x/2)dx b) √ ² ₁…

A:

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: Use the Fundamental Theorem of Calculus to compute In(tan(t²-1)) 12+A arctan (et) cos(t³) -π d dx…

A: By using the Fundamental Theorem of Calculus to compute  ddx∫-πx+4 lntanπt2-1arctanet-cost3 dt.

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

A:

Q: Evaluate the integral 1 S 2 √xe - √x sec ²³ (5e √x + 1) dx.

A: I=∫1xe−xsec2⁡(5ex+1)dx

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)…

A:

Q: a) J (te¹ + t)dt. b) fw sin(2πw)dw. c) fet cos tdt.

A: