![]() where x⋅ex 2 was integrated using the substitution u = x 2, so du = 2xdx.ĥ. The area is A(x) = base ⋅ height = x⋅ex 2. Find the volume of the solid with cross-section a rectangle of base x and height e x 2 Answerġ. where cos(x)sin 2(x) is integrated using the substitution u = sin(x), so du = cos(x) dx.Ĥ. ![]() Find the volume of the solid with circular cross-section of radius cos 3/2(x), for 0 ≤ x ≤ π/2. ![]() Recall an ellipse with semi-major axis a and semi-minor axis b has area πab, so this ellipse with semi-major axis x 2 and semi-minor axis x 3 has the area: A(x) = π⋅x 2⋅x 3 = π⋅x 5. Find the volume if the solid with elliptical cross-section perpendicular to the x-axis, with semi-major axis x 2 and semi-minor axis x 3, for 0 ≤ x ≤ 1 Answerġ. Find the volume of the solid with right isosceles triangular cross-section perpendicular to the x-axis, with base x 2, for 0 ≤ x ≤ 1 Answerġ. ![]()
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