Find the exact value of the area of the region bounded by: a y = x2, the x-axis, and x = 1 b y = sin x, the x-axis, x = 0, and x = c y = x3, the x-axis, x = 1, and x = 4 d y = ex, the x-axis, the y-axis, and x = 1 e the x-axis and the part of y =6+ x x2 above the x-axis f the axes and y = p9 x g y = 1 x , the x-axis, x = 1, and x = 4 h y = 1 x , the x-axis, x = 1, and x = 3 i y = 2 1 px , the x-axis, and x = 4 j y = ex + ex, the x-axis, x = 1, and x = 1
L34 - 6 Net Change Theorem The integral of a rate of change of a function is the net change of the function on the interval [a,b]: ▯ b ▯ F (x)dx = a ex. If the volume of water in a lake is increasing at the ▯ rate V (t), then ▯ t 2 ▯ V (t)dt = t1 gives dn ex. If a population is growing at a rate of dt ,en ▯ 2 dn dt = t1 dt gives
