# Class 12 Maths NCERT Solutions for Chapter 7 Integrals Exercise 7.7

### Integrals Exercise 7.7 Solutions

1. Integrate the functions √(4 - x2).

Solution

Let I = ∫√(4 - x2 ) dx = ∫√[(2)2 - (x)2 ]  dx

2. Integrate the functions √(1 - 4x2)

Solution

Let I = ∫√(1 - 4x2 )dx = ∫√[(1)2 - (2x)2 ]dx
Let 2x = t ⇒ 2 dx = dt
∴ I = (1/2) ∫√[(1)2 - (t)2 ] dt

3. Integrate the functions √(x2 + 4x + 6) .

Solution

4. Integrate the functions √(x2 + 4x + 1).
Solution

5. Integrate the functions √(1 - 4x - x2)
Solution

6. Integrate the functions √(x2 + 4x - 5).
Solution

7. Integrate the function √(1 + 3x - x2 )
Solution

8. Integrate the function √(x2 + 3x)
Solution

9. Integrate the functions √[1 + (x2 /9)]
Solution

10. Choose the correct answer ∫√(1 + x2 )dx is equal
(A) (x/2) √(1 + x2) + (1/2) log |[x + √(1 + x2)] + C|
(B) (2/3) (1 + x2)3/2 + C
(C) (2/3)x (1 + x2)3/2 + C
(D) (x2 /2) √(1 + x2) + (1/2) x2 log |x + √(1 + x2)| + C
Solution

Hence, the correct answer is A.

11. Choose the correct answer ∫√(x2 - 8x + 7)dx is equal to
Solution