Your friend is attempting to find the total area between y=s…

Your friend is attempting to find the total area between y=sin x and y=cos x on the interval [0,2π]{“version”:”1.1″,”math”:”[0,2π]”}. He comes up with this integral: ∫02πcosx-sinx dx{“version”:”1.1″,”math”:”∫02πcosx-sinx dx”} If he is correct, explain how he came up with this integral and evaluate it. If he is incorrect, explain what is wrong and offer a corrected expression.

a) Find the length of y=3x on the interval [1,3] by integrat…

a) Find the length of y=3x on the interval [1,3] by integration. Verify your answer using geometry. b) Set up an integral that would give the length of y=13×3{“version”:”1.1″,”math”:”y=13×3″}on the interval [0,2]. This integral is difficult to evaluate analytically. Instead of trying to evaluate it directly, write down a Riemann sum with four subintervals that could be used to estimate the integral. You do not need to do the arithmetic to evaluate the sum.