**Unformatted text preview: **( x ) . (b) Calculate g ( x ) using FTC1. (c) Calculate g ( x ) by evaluating the integral using FTC2 and then differentiating. Example 3 (Exercises 5.3.13, 5.3.15, 5.3.17, and 5.3.55 in the text) Calculate the derivatives using FTC1. 13: h ( x ) = R 1/ x 2 arctan t dt 15: y ( x ) = R tan x p t + p t dt 17: y ( x ) = R 1 1-3 x u 3 1 + u 2 du 55: y ( x ) = R x 3 p x p t sin t dt Example 4 (Exercises 5.3.19-5.3.42 in the text) Evaluate the integrals. 19: R 2-1 ( x 3-2 x ) dx 25: R 2 1 3 t 4 dt 26: R 2 π π cos θ d θ 30: R 2 ( y-1)(2 y + 1) dy 32: R π /4 sec θ tan θ d θ 33: R 2 1 (1 + 2 y ) 2 dy 39: R 1-1 e u + 1 du 40: R 2 1 4 + u 2 u 3 du 41: R π f ( x ) dx, where f ( x ) = ( sin x if ≤ x < π /2, cos x if π /2 ≤ x ≤ π ....

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