4x+12 (10 marks) Evaluate the integral. Use the proper notation with limits. S -da (x2+4)(x+5)
Evaluate the following integral. X2 + 16x-4 S*** dx x2 - 4x Find the partial fraction decomposition of the integrand. 1 * +18 x2 + 16x-4 dx = x² - 4x JOdx Evaluate the indefinite integral. *x? + 16x-4 dx = 3 х - 4x
Evaluate the given integral by changing to polar coordinates. ∫∫R(4x − y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x.
Evaluate the double integral. (x2 y)dxdy 5. 6. Use (repeated) integration by parts to find 4x cos 2xdx. Evaluate the double integral. (x2 y)dxdy 5. 6. Use (repeated) integration by parts to find 4x cos 2xdx.
21, 25 and ill like In Exercises 20-38 use a contour integral to evaluate the improper integral. (22 + 1)(x2 + 4) x +3 w (x2 + 4x + 5)2 da 23. (x2 + 1)(x2 - + 1) - J-003 + 26 da
– x2 3. (9 marks) Evaluate the integral - dx use the method X =3 sino
Question 4 5 pts x2 (A) X Ev Evaluate S 0 - 23azdy + cos,+C X (B) -cos-x+C V1-x2 -cos-x+C -r? + cos2x+c (D) - OD B ОА Question 6 5 pts + Evaluate s da. 6V22 +6 A) 3/72 +6 - 3In XV6 (B) 31n x + 12 +6 + c TV +6 2 (C) 22 +6 - 31n|a + v82 +6|+0 (D) xV22 +6 -2.101x + 4x2 +6|+c 2. 12 ОА D B Oc Question 19 5 pts...
Problem 10. (1 point) Evaluate the integral. 12 V2x2 - 4 dx = 4x
Evaluate the integral. 4) S -2x cos 7x dx Integrate the function. dx (x2+36) 3/2 5) S; 5) Express the integrand as a sum of partial fractions and evaluate the integral. 7x - 10 6) S -dx x² . 44 - 12 6)
Evaluate the following integrals. S 5x-2 dx x2-4 s 9x+25 (x+3)2 dx 2 x3+3x2-4x-12 dx x2+x-6
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...