Calculate the ratio of areas

Calculus Level 1

The image above shows a sketch of a curve y = x 2 y=x^2 within the regions − 4 ≤ x ≤ 4 -4\leq x\leq4 and 0 ≤ y ≤ 16 0\leq y\leq16 .

Let P P denote the area between this curve and the x x -axis.

Let R R denote the area of the rectangle with vertices ( − 4 , 0 ) , ( 4 , 0 ) , ( − 4 , 16 ) , ( 4 , 16 ) (-4,0),(4,0),(-4,16),(4,16) .

Find the ratio P R \dfrac PR .

1/2 1/3 1/4 2/3

Srinivasa Gopal by Srinivasa Gopal , 53, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Srinivasa Gopal
Jul 13, 2018

Equation of a parabola through the origin is y = x x , area of the parabola between -x and x is 2 * x^3 /3, area of the rectangle is 2 x x x = 2 * x^3. So the ratio of the two areas is 1/3

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...