Questions in Section Calculus II

Use trapezoidal rule to approximate the are of `sin(x^2)` from `0` to `2` using `n=10`.

Calculate `int sqrt(1-tan^2(2x)+tan^4(2x)-tan^6(2x)+...) dx`.

What is the least number of subdivisions that will guarantee, with the standard error bounds, that the result is accurate upto 4 decimal places? Consider using midpoint method to estimate the integral `int_0^0.5e^(-x^2)dx`.

Find the volume of solid obtained by revolving around the y-axis the plane area between the graph `y=1-x^2` and the x-axis.

Find the following integral: `int(x^2)/(1+x^6)dx` using substitution `u=x^(3)`.

Use Simpson's Rule to approximate `int_0^e e^(-x^2)dx` with `n=8`.

Use the Trapezoid Rule to approximate `int_0^1(dx)/sqrt(x^6+1)` with `n=6`.

Use a table of integrals to evaluate `int(dx)/(xln(x)sqrt(4+(ln(x))^2))`.

Evaluate the indefinite integral `intt(t+2)^(-6)dt`.

The demand function for a certain product is given by `p=-0.01x^2-0.2x+10`, where `p` represents the unit price in dollars and `x` is the quantity demanded measured in units of a thousand. Determine the consumer surplus if the price is set at $2.

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