1-4. Find the area of the shaded region.

(1) The curve lies above the curve and the shaded region is bounded from left side at and from the right side by the line .

(2) The curve lies above the curve . The two curves intersects at ( the shaded region bounded from left).The shaded region is bounded by the line from the right side.

(3) The shaded region is bounded by the curve from the left side and by the curve from the right side. Two curves intersects at which is the lower bound of the shaded re region and the upper bound is .

(4) The shaded region is bounded by the curve from the left side and by the curve from the rightside. The two curves intersects at which is upper bound and the lower bound is .

(5) Find the area of the shaded region by (a) integrating with respect to (b) integrating with respect to .

(a) upper curve

—–(1)

Lower curve

—–(2)

The point of intersection of two curves. Solving (1) and (2)

Thus the two curves intersects at and .

(b) The shaded region is bounded by the curve

from the right side and by the curve from the left side. and are the lower and upper limits of integration These are the -coordinates of point of intersection of the curves