**Application of integration in some cases:**

(i) General integration of vector quantity is similar to scalar quantity. Let the vector A^{→}(t) = ȋ A_{x}(t) + ĵ A_{y}(t) + ƙ A_{z} (t) be integral of a scalar variable t, then;

*∫ A ^{→}(t) dt = ȋ ∫ A_{x} (t) dt + ĵ ∫ A_{y} (t) dt + ƙ ∫ A_{z} (t) dt.*

It is called the indefinite integral of A (t).

(ii) In many cases integration is opposite to differentiation: for example-

*∫ cos x dx = sin x*

*d/dx (sin x) = cos x*

i.e., if sin x is differentiated we get cos x and if cos x is integrated we get sin x.

(iii) If a rectangle consists of innumerable elements of length x and width dy [Figure] then area of the rectangle will be, *∫ xdy = x∫ dy = xy*

(iv) If limit of width is mentioned, then area = ^{y}∫_{0} x dy = x [y]^{y}_{0} = x (y-0) = xy.