wksht4 - ESP Kouba Worksheet 4 1 Evaluate each of the...

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Unformatted text preview: ESP Kouba Worksheet 4 1. Evaluate each of the following definite integrals. 3 ‘1 Q, a. 107dx b. 1[l(x +x)dx 3 i c. Jx(x+7)2 dx (1 JWdX ‘9‘ o X+3 TT‘ e '91 e. JX2-1+X'3 dx f. Icossx dx 1 X2 0 i g. J‘x‘ll+x2 dx 0 2. Set up a definite integral which represents the area of the region below the graph of f(x) = e X 2 and above the x-axis from x = -1 to x = 2. 3. A wire lies along the x—axis from x = 1 to x = 7. It’s density at point x is given by f(x) = 1/(1 + x 2) pounds per inch. Set up a definite integral which represents the mass of the wire. 4. A snail's speed at time t (hours) is given by g(t) = 2t sin ( t 2 + 3) inches per hour. Set up a definite integral which represents the total distance traveled by the snail during the interval from t= 0 to t= 5 hours. 5. The region below the graph of y = x 2 and above the x-axis from x = O to X = 2 is revolved about the x-axis. Set up a definite integral which represents the volume of the resulting solid. 6. Differentiate each of the following functions. a. F(x)=arctan(x3) b. F(x) sin(ln(3—x)) X Jetht o _[esin2x 3]5 o :1 ii i +9 0. I ii || X 3 X e. F(x) =l et2 dt f. F(x) = II sin(t20) dt "1 7. Assume that f is acontinuous function on the interval [a, b], and let X F(x) = I f(t) dt for x in [a, b]. a a. What is F(a) ? x b. What is F(b) - (l f(t) dt) ? (L C. Is F acontinuous function ? Explain. 8. Evaluate the following limit. x+ln l 1 dt ix 1 (it lim 3 t5+1 ‘ 3 t5+l h-§O h 9. a. Sketch the region below the graph of y = x and above the graph of y=x2 from x=0 to x=1. b. Set up definite integrals which represent the volume of the solids created by revolving the region around i. the x-axis . ii. the line y = x. ...
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