Question

help me in calculus

Answer 1

\[\int\limits_{?}^{?}fg\]

Answer 2

\[\int\limits_{1}^{1}x^2\sqrt{1+x^2}dx\]

Answer 3

help me

Answer 4

When you see root signs with squares under them start thinking about trig relations. I look at this and say that we're given the two sides of a pytagorean identity under the sign:

Complete the triangle and see what you can sub out:
\[\sqrt{1+x^2} = \csc\theta \space \space \space \space (\frac{hyp}{adj})\]
\[x=\tan\theta \space \space \space \space (\frac{opp}{adj})\]
\[dx = \sec^2 \theta \space d\theta\]

make these substitutions and see where you get.

Answer 5

drawing got erased (should be before)

When you see sqrt signs with squares underneath think of pythagorean relations. Form a triangle and find the necessary substitutions: