Question 1: Please help and select the correct graph! Make answer easy to read!

EXAMPLE 5 Evaluate 8 x2 - 7x + 8 dx. x3 + 4x SOLUTION Since x3 + 4x = x(x2 + 4) can't be factored further, we write A BX + C 8 x2 - 7x + 8 x(x2 + 4) x + 1 2 + 4 Multiplying by x(x2 + 4), we have 8x2 - 7x + 8 = A(x2 + 4) + Bx + C (A + B)x2 + CX + 4A. Equating coefficients, we obtain A+ B = 8 C= -7 4A = 8. Thus A = 2 V , B = 6 , and C = -7 and so 8 x 2 - 7 x + 8 dx = x3 + 4x 1(12 X + 6 X - dx . Xz + 4 In order to integrate the second term we split it into two parts: 6 v x - 2 dx = x2 + 4 6 x2 + 4 dx - x 2 + 4 - dx . We make the substitution u = x2 + 4 in the first of these integrals so that du = 2x dx. We evaluate the second integral by means of this formula with a = 2. (Remember to use absolute values where appropriate.) 8 x2 - 7x + 8 dx = 2 dx + 6x x (x2 + 4 ) x2 + 4 dx - x2 + 4 dx = 2 ln(x) + Inx- + 4 4 -tan + K X3 EXAMPLE 1 Find f7X+18de. X _ SOLUTION Since the degree of the numerator is greater than the degree of the denominator, we first perform the long division. This enables us to write the following. (Remember to use absolute values where appropriate.) 15 3 X1 \f\fFind the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3 sin(x), y = 3 cos(x), O S x S 7/4; about y = -1 V = 6V2 - N / CO