TS Inter 2nd Year Maths 2B Solutions Chapter 7 Definite Integrals Ex 7(a)

Students must practice this TS Intermediate Maths 2B Solutions Chapter 7 Definite Integrals Ex 7(a) to find a better approach to solving the problems.

TS Inter 2nd Year Maths 2B Solutions Chapter 7 Definite Integrals Exercise 7(a)

I. Evaluate the following integrals as the limit of a sum.

Question 1.
\(\int_0^5(x+1) d x\)
Solution:
We use the following formula for p = 5
and f(x) = x² + 1, x ∈ [0, 5] and f is continuous over [0, 5].

Question 2.
\(\int_0^4 x^2 d x\)
Solution:

II. Evaluate the following integrals as the limit of a sum.

Question 1.
\(\int_0^4\left(x+e^{2 x}\right) d x\)
Solution:
Here p = 4, and f(x) = x + e^2x

Question 2.
\(\int_0^1\left(x-x^2\right) d x\)
Solution:
Here p = 1 and f(x) = x – x²