Find the positive value of c such that the area of the region bounded by the par

Question

Explanation / Answer

solution: First, find where they intersect: x^2 - c^2 = c^2 - x^2 2x^2 = 2c^2 x^2 = c^2 x = c They intersect at (-c , 0) and (c , 0). Along this interval y = c^2 - x^2 will be greater than y = x^2 - c^2 so, int( (c^2 - x^2) - (x^2 - c^2) dx , x = -c , x = c) int(c^2 - x^2 - x^2 + c^2 dx , x = -c , x = c) int(2c^2 - 2x^2 dx , x = - c , x = c) => 2 * int(c^2 - x^2 * dx , x = - c , x = c) = 576 => 2 * (x * c^2 - (1/3) * x^3) , x = -c , x = c) = 576 => 2 * (c * c^2 - (1/3) * c^3) - 2 * (-c * c^2 - (1/3) * (-c^3)) = 576 => 2 * (c^3 - (1/3) * c^3) - 2 * (-c^3 + (1/3) * c^3) = 576 => 2 * ((2/3) * c^3) - 2 * ((-2/3) * c^3) = 576 => (4/3) * c^3 + (4/3) * c^3 = 576 => (8/3) * c^3 = 576 (8/3) * c^3 = 576 c^3 = 576 * 3 / 8 c^3 = 24 * 24 * 3 / 8 c^3 = 3 * 8 * 24 * 3 / 8 c^3 = 9 * 24 c^3 = 9 * 3 * 8 c^3 = 27 * 8 c^3 = 3^3 * 2^3 c = 3 * 2 c = 6 we find c = 6=answer

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.