Calculus

Arc Length and Surface Area

Surface Area by Integration

         

The area of the surface obtained by revolving the curve y=x y = \sqrt{x} , 4x7 4 \leq x \leq 7 , about the x x -axis can be represented by π6(aabb) \frac{\pi}{6}(a \sqrt{a} - b \sqrt{b}) . What is the value of a+b a + b ?

The area of the plane 3x+2y+z=30 3x+2y+z = 30 , where x0x \geq 0, y0y \geq 0 and z0z \geq 0 can be represented by aba \sqrt{b}, where aa and bb are positive integers and bb is not divisible by the square of a prime. What is the value of a+ba+b?

What is the area of the surface obtained by revolving the curve y=81x2y=\sqrt{81-x^2} from 2x2 -2 \leq x \leq 2 about the x x -axis?

Let SS be the surface area of the solid obtained by rotating the curve y=x3 y = x^3 (0x1)( 0 \leq x \leq 1) about the x x -axis. If S=π27(aa1)S = \frac{\pi}{27}(a \sqrt{a} - 1) , where aa is a positive integer, what is the value of a a ?

The area of the paraboloid z=x2+y2 z = x^2 + y^2 , where 0z121 0 \leq z \leq 121 , can be represented by π6(aa1) \frac{\pi}{6} (a \sqrt{a} - 1) . What is the value of aa?

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