Application of Integrals

- Area of the region bounded by the curve
*y*=*f*(*x*),*x*-axis, and the lines*x = a*and*x = b*(*b*>*a*) is given by or - The area of the region bounded by the curve
*x*=*g*(*y*),*y*-axis, and the lines*y = c*and*y = d*is given by or - If a line
*y = mx + p*intersects a curve*y*=*f*(*x*) at*x = a*and*x = b*, (*b*>*a*), then the area (*A*) of region bounded by the curve*y*=*f*(*x*) and the line*y = mx + p*is

- If a line
*y = mx + p*intersects a curve*x*=*g*(*y*) at*y = c*and*y = d*,(*d*>*c*), then the area (*A*) of region bounded by the curve*x*=*g*(*y*) and the line*y = mx + p*is

**Example 1: **Find the area of the region in the first and third quadrant enclosed by the *x*-axis and the line , and the ellipse

**Solution: **The given equations are

... (1)

... (2)

Substituting in equation (2), we obtain

Hence, the line meets the ellipse at C and D in the first and third quadrant respectively.

In the figure, CM ⊥ XX′

Now, area OCMO =

Area ACMA

- The area of the region enclosed bet…

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