Integration Lecture 6

Integration is the :

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

"If"int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C where, C is a constant of integration, then the function f(x) is equal to

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 :

Using the concept of integration evaluate an area by definite integral

Using integration, find the area of the triangle ABC, coordinates of whose vertices are A(4,1), B(6,6) and C(8,4)

Sketch the graph of y=|x+4|. Using integration find the area of the region bounded by the curve y=|x+4| and x= -6 and x=0.

Using integration, find the area of the region: {(x , y):9x^2+y^2lt=36\ "and"\ 3x+ygeq6}

Using integration, find the area of the triangle PQR, coordinates of whose vertices are P(2, 0), Q(4, 5) and R(6, 3).

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).