Integration Lecture 5

Integration is the :

Let I_n=int tan^n x dx, (n>1) . If I_4+I_6=a tan^5 x + bx^5 + C , Where C is a constant of integration, then the ordered pair (a,b) is equal to :

If the integral I= ∫e^(5ln x)(x^(6)+1)^(-1)dx=lamdaln (x^(6)+1)+C , (where C is the constant of integration) then the value of (1)/(lambda) is

Using the concept of integration evaluate an area by definite integral

Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2), (1, 5) and (3, 4).

Using integration, find the area of the region bounded by the triangle whose vertices are (2,1), (3, 4) and (5,2).

Using integration, find the area of the triangle ABC whose vertices are A(-1,1), B(0,5) and C(3,2) .

If introot(3)(x).root(5)(1+root(3)(x^(4)))dx=5/8(1+x^(4/a))^((2a)/b)+c (where c is constant of integration), then value of (a+b) is

If int x^(5)e^(-x^(2))dx = g(x)e^(-x^(2))+C , where C is a constant of integration, then g(-1) is equal to

Using integration, find the area of the region bounded by the line 2y=5x+7 , x-axis and the lines x = 2 and x = 8.