College Calculus II Recitation Related to Section 7 4 Partial Fraction Decomposition Completing the Square 1 Completing the Square We have the following x2 bx c x2 bx b2 4 b2 4 c x2 bx b2 4 c cid 18 cid 18 b2 4 cid 19 cid 19 2 b2 4 b 2 x c Example 1 For each of the following write the polynomial in the form cid 0 x a2 2 a3 cid 1 a1 for suitable constants a1 a2 and a3 a x2 4x 10 b x2 8x 18 c x2 2x 3 e 2x2 6x 9 d 2x2 4x 10 Hint Is there a common factor that can be factored out rst Page 1 of 4 College Calculus II Recitation Related to Section 7 4 Partial Fraction Decomposition Example 2 Evaluate the following Show all work a Let a be a nonzero constant cid 90 1 x2 a2 dx cid 90 cid 90 cid 90 1 b x2 4x 10 dx 1 c 2x2 4x 10 dx d 2x2 6x 9 dx 1 Page 2 of 4 College Calculus II Recitation Related to Section 7 4 Partial Fraction Decomposition Example 3 To evaluate the following integral would it help to complete the square in the denominator rst Explain cid 90 1 x2 6x 8 dx Long Division Example 4 Write the following in the form where the degree of R x is strictly less than the degree of Q x S x R x Q x x3 1 x 1 a b x3 5 x 1 Page 3 of 4 College Calculus II Recitation Related to Section 7 4 Partial Fraction Decomposition x5 8x 1 x2 2 c d x5 2x2 3 6x7 3x4 Page 4 of 4