Class 12 Maths NCERT Solutions for Chapter 7 Integrals Exercise 7.7

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

NCERT Solutions for Chapter 7 Integrals Class 12 Maths Exercise 7.7