3. Evaluate the integral sin^5x cos^3x dx , interval [pi/2, 3pi/4]

14. Evaluate the integral (x^3)/sqrt(16-x^2) dx, interval [0, 2sqrt3]

19. Evaluate the integral 1/(x^2-1) dx, interval [2, 3]

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6. Use midpoint rule and simpsons rule to approximate the given integral with the specified value of n.

e^(-srt(x)) dx, interval [0,1] n=6

8. Use the trapezoidal rule and the midpoint rule and the simpsons rule to approximate the given integral with the specified vaule of n.

sin(x^2)dx, interval [0, 1/2] n=4

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Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

6. 1/(2x-5) dx, interval [0, -infinity]

20. lnx/x^3 dx, interval [1, infinity]

30. dx/sqrt(1-x^2), interval [0,1]

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4. Functions given x=y^2 - 4y and x=2y - y^2 points of cross over (-3,3) and (0,0). Find the area of which curves overlap.

14. Sketch the region enclosed by the given curves. Decide whether to intergrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the are of the region.

y=singx, y=2x/pi , x is greater of equal to 0

38. Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis.

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8. Find the volume of the solid obtained by rotating the region bounded by the given curvbes about the specified line. Sketch the region, the solid, and a typical disk or washer.

y=x^(2/3), x=1, y=0, about the y-axis

22. Each integral represents the volume of a solid. Describe the solid.

a. pi y dy, interval [2,5] b. pi [(1+cosx)^2 - 1^2]dx, interval [0,pi/2]

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1. Use the arc length formula (2) to find the length of the curve y=2-3x, interval [-2,1]

formula L = sqrt [ 1+ (dy/dx)^2 ] dx interval [a,b]

8. Graph teh curve and find its exact length.

y=(x^2)/2 - (lnx)/4, interval from 2 to 4

20. Use either a CAS or a table of integrals to find the exact length of the curve.

y = lnx interval from 1 to sqrt(3)

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Please explain how to do these problems, no need for solutions but if you have some spare time it would be helpful.

Thank you