In this page integration worksheet2 solution7 we are going to see
solution of some practice question from the worksheet of integration.

**Question 7**

(i) Integrate the following with respect to x , cosec (2 - x) cot (2 - x)

**Solution:**

The given question exactly matches the formula

**∫ cosec (a x + b) cot (a x + b) = - (1/a) cosec (a x + b) + C**

Now we are going to integrate the given question by using this formula in the question instead of "a" we have -1

So we get,

∫cosec (2 - x) cot (2 - x) dx = -(1/-1) cosec (2 - x) + C

= cosec (2 - x) + C

(ii) Integrate the following with respect to x ,cosec (4 x + 2) cot (4 x + 2)

**Solution:**

The given question exactly matches the formula

**∫ cosec (a x + b) cot (a x + b) = - (1/a) cosec (a x + b) + C**

Now we are going to integrate the given question by using this formula in the question instead of "a" we have 4

So we get,

∫cosec (4 x + 2) cot (4 x + 2) dx = -(1/4) cosec (4 x + 2) + C

= -cosec (4 x + 2)/4 + C

(iv) Integrate the following with respect to x ,cosec (3 - 2 x) cot (3 - 2 x)

**Solution:**

The given question exactly matches the formula

**∫ cosec (a x + b) cot (a x + b) = - (1/a) cosec (a x + b) + C**

Now we are going to integrate the given question by using this formula in the question instead of "a" we have -2

So we get,

∫cosec (3 - 2 x) cot (3 - 2 x) dx = -(1/-2) cosec (3 - 2 x) + C

= cosec (3 - 2 x)/2 + C

(iv) Integrate the following with respect to x , cosec (L x + m) cot (L x + m)

**Solution:**

The given question exactly matches the formula

**∫ cosec (a x + b) cot (a x + b) = - (1/a) cosec (a x + b) + C**

Now we are going to integrate the given question by using this formula in the question instead of "a" we have L

So we get,

∫cosec (L x + m) cot (L x + m) dx = -(1/L) cosec (L x + m) + C

= - cosec (L x + m)/L + C

integration worksheet2 solution7 integration worksheet2 solution7

- Back to worksheet
- Integration
- Substitution method
- Decomposition method
- Properties of integrals
- Integration-by parts
- Integration-of Sec³ x
- Standard integrals
- Integrating quadratic denominator
- Integration-using partial fractions
- Definite integrals