Find the area bounded by x = at², y = at between the ordinates corresponding to t = 1 and t = 2

Using integration, find the area of the triangle with sides y = 2x + 1, y = 3x + 1 and x = 4.

Find the area of the curve y²=(x-5)²(x-6) between
(i) x=5 and x=6
(ii) x=6 and x=7

Find the ratio of the area between the curves y=cosx and y=cos2x and x- axis from x=0 to \(x=\frac { \pi }{ 3 } \)

Find the value of ‘c’ for which the area bounded by the curve y=8x²-x⁵,the lines x=1,x=c and x-axis \(\frac { 16 }{ 3 } \)