Evaluate the following integrals using Green's theorem. 8. S. (2y2 + xsin(x)dx + (x3 - evy)dy where c is the rectangle in R2 with vertices at (1,0), (2,0), (2,2) and (1,2) oriented counterclockwise.
Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C for the constant of integration.) Evaluate the integral. (Use C for the constant of integration.) cos 498(3y) sin?(3y) dy
8. Evaluate the indefinite integral: S(5x3 + 2 cos x )dx a. b. S(4x3 – 8x + 7) dx
6. Use the method of partial fractions to evaluate the indefinite integral. 8x' + 13x •dx (x + 2) 7. Consider a. Using complete sentences, explain why the integral is improper. b. Evaluate the improper integral to determine its convergence or divergence.
Q2- Evaluate the integrals: (a) ſ sinᵒ x.cos x. dx (b) ſ sin 8x. sin 5x.dx
8. Evaluate $c (4xy3 + 3y) dx + (8x – 6x?y?) dy where C is the triangle formed by vertices (0, 0), (3,0), (3, 4) oriented counterclockwise
Evaluate the integral 1 (8x+3)(x2 + 2x - 1)3 dx Round your answer to one decimal point, if necessary.
Evaluate I=∫C(sinx+9y)dx+(8x+y)dy for the nonclosed path ABCD in the figure. A=(0,0),B=(4,4),C=(4,8),D=(0,12) (1 point) Evaluate I figure. Je(sin x +9y) dx + (8x + y) dy for the nonclosed path ABCD in the A (0,0), B (4,4, C (4,8), D (0,12)
Evaluate the following integral 8x +x+33 + 1)(x +4 dx Can partial fraction decomposition be used to evaluate the given integral? Select the correct choice below and, if necessary, fill in the answer box to complete your choice ОА Yes, partial fraction decomposition can be used. The given integral can be rewritten as ( dx, which is more readily evaluated OB. No, partial fraction decomposition cannot be used Evaluate the indefinite integral &x?+x+39 s dx = 0
Find f x'e-s2 dx = S re-8x dx = S x4e-s2 d.x = sx"e-se dx = Now, find L (x) =