# wewer - f x = x 3 and g x = √ x[15 pts 3(a Use...

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MATH 140: Exam 4 Thursday, December 6, 2007 Show all work and justify your answers. Your solutions should read nicely and be legible. They should not be composed of regurgitated fragments of your mind scattered about the page. 1. (a) Let f ( x ) = sin( x ) and let P be the partition of the interval [0 , 2 π ] deﬁned by P = { 0 , π 6 , π 2 , 5 π 6 , π } . Compute L f ( P ). [15 pts] (b) Let h ( x ) be any continuous function that satisﬁes - 4 h ( x ) x 2 - 4 for 0 x 1. Find upper and lower bounds for Z 1 0 x 3 h ( x ) dx [15 pts] 2. Find the area of the bounded region between the graphs
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Unformatted text preview: f ( x ) = x 3 and g ( x ) = √ x . [15 pts] 3. (a) Use Logarithmic Diﬀerentiation to ﬁnd f ( x ) when f ( x ) = x 3 / 2 e-( x 2 ) 1-e x [15 pts] (b) Evaluate d dx Z sin( x ) x 2 ln | t | dt [10 pts] 4. Evaluate the following: (a) Z x 2 √ x-1 dx [10 pts] (b) Z 2-3 x + | x | dx [10 pts] (c) Z 1 1 + e x x + e x dx [10 pts] 5. Find the average height of a castle door bounded by the parabola y = 4-x 2 and the x-axis. [Bonus 5 pts]...
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