Chapter 5 Integration Miscellaneous Exercise 5 Solutions

Balbharati Maharashtra State BoardStd 12 Commerce Statistics Part 1 Digest PdfChapter 5 Integration Miscellaneous Exercise 5 Questions and Answers.

Maharashtra State Board 12th Commerce Maths Solutions Chapter 5 Integration Miscellaneous Exercise 5

(I) Choose the correct alternative from the following:

(II) Fill in the blanks.

(III) State whether each of the following is True or False:

(IV) Solve the following:

1. Evaluate:

(i)
Solution:

(ii)
Solution:

(iii)
Solution:

(iv)
Solution:

(v) If f'(x) = √x and f(1) = 2, then find the value of f(x).
Solution:
By the definition of integral

(vi) ∫|x| dx if x < 0
Solution:
∫|x| dx = ∫-x dx …..[∵ x < 0]
= -∫x dx
= + c

2. Evaluate:

(i) Find the primitive of
Solution:
Let I be the primitive of

(ii)
Solution:

(iii)
Solution:

(iv)
Solution:

(v)
Solution:

3. Evaluate:

(i)
Solution:

(ii)
Solution:

(iii)
Solution:

(iv)
Solution:

(v)
Solution:

(vi)
Solution:

(vii)
Solution:

(viii)
Solution:

4. Evaluate:

(i) ∫(log x)²dx
Solution:

(ii)
Solution:

(iii) ∫x e^2xdx
Solution:

(iv) ∫log(x²+ x) dx
Solution:

(v)
Solution:

(vi)
Solution:

(vii)
Solution:

5. Evaluate:

(i)
Solution:

(ii)
Solution:

(iii)
Solution: