integration worksheet6 solution1

Integration Worksheet6 solution1

In this page integration worksheet6 solution1 we are going to see solution of some practice question from the worksheet of integration.

Question 1

Integrate the following with respect to x, x e^-x

Solution:

Here we are going to use the method partial differentiation to integrate the given question.

∫ x e^-x dx

∫ u dv = u v - ∫ v du

u = x dv = e^-x

du = dx v = - e^-x

= ∫ x e^-x dx

= x ( - e^-x) - ∫ (- e^-x) dx

= - x e^-x + ∫ e^-x dx

= - x e^-x - e^-x + C

= -e^-x (x + 1) + C

Question 2

Integrate the following with respect to x, x cos x

Solution:

Here we are going to use the method partial differentiation to integrate the given question.

∫ x cos x dx

∫ u dv = u v - ∫ v du

u = x dv = cos x

du = dx v = sin x

= ∫ x cos x dx

= x (sin x) - ∫ sin x dx

= x (sin x) - (- cos x) + C

= x sin x + cos x + C

Question 3

Integrate the following with respect to x, x cosec ²x

Solution:

Here we are going to use the method partial differentiation to integrate the given question.

∫ x cosec ²x dx

∫ u dv = u v - ∫ v du

u = x dv = cosec ²x

du = dx v = -cot x

= ∫ x cosec ²x dx

= x (-cot x) - ∫ -cot x dx

= - x cot x + ∫ (cos x/sin x) dx

= - x cot x + log (sin x) + C

Question 4

Integrate the following with respect to x, x sec x tan x dx

Solution:

Here we are going to use the method partial differentiation to integrate the given question.

∫x sec x tan x dx

∫ u dv = u v - ∫ v du

u = x dv = sec x tan x

du = dx v = sec x

= ∫ x sec x tan x dx

= x (sec x) - ∫sec x dx

= x sec x - log (sec x + tan x) + C

integration worksheet6 solution1 integration worksheet6 solution1

SBI!