Gujarat Board GSEB Textbook Solutions Class 12 Maths Chapter 7 Integrals Ex 7.8 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Integrals Ex 7.8

Evaluate the following definite integrals as limits of the sum:

Question 1.

\(\int_{a}^{b}\) x dx

Solution:

Question 2.

\(\int_{5}^{0}\) (x + 1) dx

Solution:

Compare \(\int_{5}^{0}\) (x + 1) dx with \(\int_{b}^{a}\) f(x) dx, we have:

f(x) = x + 1, ‘a’ = 0, ‘b’ = 5 and nh = b – a = 5 – 0 = 5.

Now, f(a) = f(0) = 0 + 1 = 1

f(a + h) = f(h) = h + 1 = 1 + h

f(a + 2h) = f(2h) = 2h + 1 = 1 + 2h

Question 3.

\(\int_{-3}^{2}\) x^{2} dx

Solution:

Question 4.

\(\int_{-4}^{1}\) (x^{2} – x) dx

Solution:

Question 5.

\(\int_{1}^{-1}\) e^{x} dx

Solution:

Question 6.

\(\int_{4}^{0}\) (x + e^{2x}) dx

Solution: