Question

Use areas to evaluate the integral. integral_a⁷ b 2s ds, 0 < a< b integral_a⁷ b 2s ds =

Answer 1

To evaluate the integral ∫ab 2s ds, find the area bounded by the curve y = 2s and the x-axis between the limits a and b. The integral is equal to (b - a) * b.

Step-by-step explanation:

To evaluate the integral ∫ab 2s ds, we need to find the area bounded by the curve y = 2s and the x-axis between the limits a and b. Since the integrand is 2s, the area under the curve is given by the formula for the area of a triangle: A = 1/2 * base * height. In this case, the base is b - a and the height is 2b. Therefore, the integral is equal to 1/2 * (b - a) * 2b = (b - a) * b.