Class 12 Maths NCERT Solutions for Chapter 7 Integrals Exercise 7.8

1. Evaluate the following definite integrals as limit of sums.

∫_a^b x dx

Solution

It is known that,

2. Evaluate the following definite integrals as limit of sums.
∫_a^b (x + 1) dx

Solution

Let I = ∫_a^b (x + 1) dx
It is known that,

Here, a = 0, b = 5, and f(x) = (x + 1)
⇒ h = (5 - 0)/n = 5/n

3. ∫₂³ x² dx

Solution

It is known that,

Here, a = 2, b = 3, and f(x) = x²
⇒ h = (3 - 2)/n = 1/n

4. ∫₂³ (x² - x) dx

Solution

a = 1, b = 4, and f(x) = x²
∴ h = (4 - 1)/n = 3/n

= 3[1 + 3 + 3]
= 3(7)
I₁ = 21 ...(2)

a = 1, b = 4, and f(x) = x
⇒ h = (4 -1)/n = 3/n

From equations (2) and (3), we obtain

I₂ = 15/2 ...(3)
From equations (2) and (3), we obtain

I = I₁ + I₂ = 21 - 15/2 = 27/2

5. Evaluate the following definite integrals as limit of sums ∫_-1¹ e^x dx

Solution

6. Evaluate the following definite integrals as limit of sums ∫₀⁴ (x + e^2x ) dx

Solution

It is known that ,

Here, a = 0, b = 4, and f(x) = x + e^2x
∴h = (4 - 0)/n = 4/n

NCERT Solutions for Chapter 7 Integrals Class 12 Maths Exercise 7.8