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.