-0.2 -0.4 -0.6 -0.8 -1 0 1 4 5 CO 6 7 N 3 x [rad] King Hiero, Archimedes friend, wants to know the volume of a revolute crown. Without submerging it in water, what is the volume of a crown with the shape shown in the figure in bold, revolved around the y-axis? (Hint: Where are cos(x) and sin(x) equal?) Your I dont know

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).