63. Verify the formula Tr. (x – x1)(x – x2) dx = =(x1 – x2)3 Then prove that the solid obtained by rotating the shaded region in Figure 19 about the x-axis has volume V = BH?, with B and H as in the figure. Hint: Let xj and x2 be the roots of f(x) = ax +b – (mx + c)*, where x < x2. Show that x2 f(x) dx and use Eq. (1). y= MI +e = ax + b FIGURE 19 The line y = mx + c intersects the parabola y2 = ax +b at two points above the x-axis.

Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

A:

Q: 4. Let f(x) = x, Vx E [0, b]. Show that f is integrable and that 62 f(x) dx : Answer:

A: Given function is  fx=x, ∀ x∈0,b

Q: 2. / x + 4x x + 4x +13 dx

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: Draw a sketch of the cylinder z = -4 - y2.

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: 2. Use symmetry to evaluate the given integrals. -200 A) S, 2x5 dx -200 В) cos х -п/4 B) S"/ cOS x…

A: A) ∫-2002002x5 dxB) ∫-π4π4 cos x dx