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

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}) x² dx
Solution:

Question 4.
(int_{-4}^{1}) (x² – x) dx
Solution:

Question 5.
(int_{1}^{-1}) e^x dx
Solution:

Question 6.
(int_{4}^{0}) (x + e^2x) dx
Solution: