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.
\(\int_{-3}^{2}\) x2 dx
Solution:
Question 4.
\(\int_{-4}^{1}\) (x2 – x) dx
Solution:
Question 5.
\(\int_{1}^{-1}\) ex dx
Solution:
Question 6.
\(\int_{4}^{0}\) (x + e2x) dx
Solution:
