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Integration by parts technique is used to solve problems in a simple way with complete steps. Evaluate the integral. Integrating by parts Here 2. Here Formula integration by parts: integrating by parts 3. Integrating by parts Again … Read more
1-30 Evaluate the integrals by making appropriate u-substitution. Let then (1) be comes Integrating w.r.t , we get 2. then (1) becomes From (2) Substituting into (3), we get 3. … Read more
1-4 Find the area of the surface generated by revolving the given curve about the -axis. 1. differentiating w.r.t Formula for the area of the Surface of revolution ( about -axis): Substituting (1) and (2) into (3) and integrating over the interval 2. differentiating … Read more
Use the Theorem of Pythagoras to find the length of the line segment from to , and confirm that the value is consistent with the length computed using (a) Formula (4) (b) Formula (5). Solution: Given points are and . (a) Formula (4) is given by Equation of the line … Read more
1-4 use cylindrical shells to find the volume of the solid generated when the shaded region is revolved about the indicated axis. (1) (2) solving and simultaneously (3) (4) Solving … Read more
Find the volume of the solid that results when the shaded region is revolved about the indicated axis. (1) (2) (3) Solving for (4) Solving for when , then : (5) … Read more
1-4. Find the area of the shaded region. (1) The curve lies above the curve and the shaded region is bounded from left side at and from the right side by the line . (2) The curve lies above the curve . The two curves intersects at ( the shaded region bounded … Read more
Question 1. Evaluate. (a) (b) (c) (d) (e) (f) Question 2. (a) (b) (c) (d) (e) (f) Questions 3-8. Write each expression in sigma notation but do … Read more
EXERCISE Evaluate the integrals using appropriate Substitutions then the above integral becomes From (1) substituting into (2). then the integral (1) becomes Now substituting into (3) Then the above integral becomes Substituting into (1) … Read more
In this section, we shall develop the concept of antiderivatives. It contains solutions to integration problems. (1) — In each part, confirm that the formula is correct…. (a) corresponding integration formula: (b) Corresponding integration formula: (2)—In each part, confirm that the stated formula is correct by differentiating. … Read more