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scott,Each person contributing should probably...

scott,Each person contributing should probably just post a solution to one problem, unless perhaps they have a question on another and would like to show a few of their steps. As always, try to show the clearest steps that you can so we can follow your thinking!

Problem 1:

Integral(cuberoot(x), 1, 8), that is

the definite integral from 1 to 8 of the cube root(x) dx.

Problem 2:

Integral (-xe^(-x^2), -2, 0), rounded to two decimal places.

Problem 3:

Integral (3cos^3(x))/[1 – sin^2(x)], 0, PI/6)

Note “cos^3(x)” means (cos x)^3.

You can use your calculator if necessary to evaluate or simplify your final answer, but ideally you should probably be able to get an exact answer by hand since 0 and pi/6 are special angles in radians; you could then put your exact answer in your calculator to show it in decimal form too.

Hint: simplify this by rewriting the denominator using a trig identity, and then go from there.

Problem 4:

Use a Riemman sum to approximate the area under the graph of f(x) on the given interval, with selected points as specified.

F(x) = 4x^2 ; interval 0 <= x <= 2, n = 4, using left endpoints.

Problem 5:

Find the area under the following curve: y = 8x^3 between x = 0 to x = 2.

Problem 1:

Integral(cuberoot(x), 1, 8), that is

the definite integral from 1 to 8 of the cube root(x) dx.

Problem 2:

Integral (-xe^(-x^2), -2, 0), rounded to two decimal places.

Problem 3:

Integral (3cos^3(x))/[1 – sin^2(x)], 0, PI/6)

Note “cos^3(x)” means (cos x)^3.

You can use your calculator if necessary to evaluate or simplify your final answer, but ideally you should probably be able to get an exact answer by hand since 0 and pi/6 are special angles in radians; you could then put your exact answer in your calculator to show it in decimal form too.

Hint: simplify this by rewriting the denominator using a trig identity, and then go from there.

Problem 4:

Use a Riemman sum to approximate the area under the graph of f(x) on the given interval, with selected points as specified.

F(x) = 4x^2 ; interval 0 <= x <= 2, n = 4, using left endpoints.

Problem 5:

Find the area under the following curve: y = 8x^3 between x = 0 to x = 2.

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