Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 2 Integral Calculus I Miscellaneous Problems Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Miscellaneous Problems

Question 1.

∫\(\frac { 1 }{\sqrt{x-1}-\sqrt{x+3}}\) dx

Solution:

∫\(\frac { 1 }{\sqrt{x+2}-\sqrt{x+3}}\) dx

Conjugating the Denominator

Question 2.

∫\(\frac { dx }{2-3x-2x^2}\)

Solution:

Question 3.

∫\(\frac { dx }{e^x+6+5e^{-x}}\)

Solution:

Question 4.

∫\(\sqrt { 2x^2-3}\) dx

Solution:

Question 5.

∫\(\sqrt { 9x^2+12x+3}\) dx

Solution:

Question 6.

∫(x + 1)² log x dx

Solution:

∫udv = uv – ∫vdu

∫(x + 1)² log x dx

Question 7.

∫log (x – \(\sqrt { x^2-1}\)) dx

Solution:

Question 8.

\(\int_{0}^{1}\) \(\sqrt { x(x-1)}\) dx

Solution:

Question 9.

\(\int_{-1}^{1}\) x² e^{-2x} dx

Solution:

Question 10.

\(\int_{0}^{3}\) \(\frac { xdx }{\sqrt {x+1} + \sqrt{5x+1}}\)

Solution: