Find the area bounded by the curve y=xe^x and y=xe^-x and the line x=1.

Find the area of the region bounded by y=e^x and y=e^-x and the;line x=1.

Find the area of the region bounded by a²y²=a²(a²-x²)

Find the area of the region enclosed by the two circles x²+y²=1 and (x-1)²+y²=1.

AOB is the positive quadrant of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\cfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) where OA=a and OB=b.Find the area between the arc AB and chord AB of the elipse.

Show that the ratio of the area under the curve y=sinx and y=sin2x between x=0 and \(x=\frac { \pi }{ 3 } \) and x- axis are as 2 : 3.

Find the area bounded by the curve y2(2a-x)=x² and the line x=2a.

Find the area bounded by the curve xy2=a2(a-x) and the y-axis

Find the area enclosed by the parabolas 5x²-y=0 and 2x²-y+9=0.

Find the area of the region bounded by the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\)

Find the area of the region in the first quadrant enclosed by the x axis, the line y = x and the circle x² + y² = 32

In the given figure, \(\Delta\)OBA is the part of the ellipse 9x² + y² = 36 in the first quadrant such that OA = Z and OB = 6. Find the area between the arc AB and chord AB.

Find the area of the region bounded by the parabola y = x² and the curve y = |x|

Find the area bounded by the curve |x| + |v| = 1 using integration.

Draw a rough sketch of the curve y = I + |x +1|, x = -3, x = 3 and y = 0 and find the area of the region bounded by them using integration.