In this page integration worksheet2 solution4 we are going to see
solution of some practice question from the worksheet of integration.

**Question 4**

(i) Integrate the following with respect to x , sin (x + 3)

**Solution:**

The given question exactly matches the formula

**∫sin (a x + b) = - (1/a) cos (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,

∫ sin (x + 3) dx = -(1/1) cos (x + 3) + C

= - cos (x + 3) + C

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

**Solution:**

The given question exactly matches the formula

**∫sin (a x + b) = - (1/a) cos (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,

∫ sin (2 x + 4) dx = -(1/2) cos (2 x + 4) + C

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

(iii) Integrate the following with respect to x ,sin (3 - 4 x)

**Solution:**

The given question exactly matches the formula

**∫sin (a x + b) = - (1/a) cos (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,

∫ sin (3 - 4 x) dx = -(1/4) cos (3 - 4 x) + C

= - cos (3 - 4 x)/4 + C

(iv) Integrate the following with respect to x , cos (4 x + 5)

**Solution:**

The given question exactly matches the formula

**∫cos (a x + b) = (1/a) sin (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,

∫ cos (4 x + 5) dx = (1/4) sin (4 x + 5) + C

= sin (4 x + 5)/4 + C

(v) Integrate the following with respect to x ,cos (5 - 2 x)

**Solution:**

The given question exactly matches the formula

**∫cos (a x + b) = (1/a) sin (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,

∫ cos (5 - 2 x) dx = (1/2) sin (5 - 2 x) + C

= sin (5 - 2 x)/2 + C

integration worksheet2 solution4 integration worksheet2 solution4

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- 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