Leadership

Mathematics

Twelve Standard

Test your understanding of this lesson Formula for differentiation to integration | on inverse trigonometry:-

1)
The value of \(\int \frac{\text{d}x}{{(1+x^{2})}tan^{-1}x}\) is
  • \(log|tan^{-1}x|+c\)
  • \(\frac{1}{2}(tan^{-1}x)^{2}+c\)
  • \(log|1+x^{2}|+c\)
  • None of these
2)
\(\frac{sin^{3}x}{(1+cos^{2}x)\sqrt{1+cos^{2}x+cos^{4}x}}dx\) is equal
  • \(tan^{-1}(secx+tanx)+c\)
  • \(sec^{-1}(secx+tanx)+c\)
  • \(sec^{-1}(secx+cotx)+c\)
  • \(tan^{-1}(secx+cotx)+c\)
3)
If \(f(x)=\sqrt{x}\) and \(\phi(x)=e^{x}-1\), then \(\int (fog)(x)dx\) is equal to
  • \(2\sqrt{e^{x}-1}\)+2tan^{-1}(e^{x}-1)+c\)
  • \(2\sqrt{e^{x}-1}-2tan^{-1}(\sqrt {e^{x}-1})+c\)
  • \(2\sqrt{e^{x}-1}\)-2tan^{-1}(e^{x}-1)+c\)
  • \(2\sqrt{e^{x}-1}+2tan^{-1}(\sqrt {e^{x}-1})+c\)
4)
\(\int \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}\frac{\text{d}x}{x}=2cos^{-1}(\sqrt{x})-\phi(x)+c\), Then \(\phi(x)\) is equal to
  • \(2\log\Big(\frac{1+\sqrt{1-x}}{\sqrt{x}}\Big)\)
  • \(2\log\Big(\frac{1-\sqrt{1-x}}{\sqrt{x}}\Big)\)
  • \(2\log\Big(\frac{1-\sqrt{1+x}}{\sqrt{x}}\Big)\)
  • \(2\log\Big(\frac{1-\sqrt{1-x}}{\sqrt{x}}\Big)\)
5)
\(\int \frac{(sin^{-1}x)^{2}}{\sqrt{1-x^{2}}}dx\) is
  • \(\frac{1}{3}(sin^{-1}x)^{3}+c\)
  • \((sin^{-1}x)^{3}+c\)
  • \(\frac{1}{3}(cos^{-1}x)^{3}+c\)
  • None of these
Hand draw

You may like this videos

All rights reserved © 2025 tubelessons.net

Hide

Forgot your password?

Close

Error message here!

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close