# Class: subject: hence evaluate (i) ∫x2+1​dx or (ii)) ∫x2+4x+6​dx $\begi.. Integral of x sqrt(x+1) Integral of x sqrt(x+1) Question Question asked by Filo student Class: subject: hence evaluate (i) or (ii)) \[ \begin{array}{l} \therefore I=\sqrt{x^{2}+a^{2}} \int 1 d x-\int\left[\frac{d\left(\sqrt{x^{2}+a^{2}}\right)}{d x} \cdot \int 1 d x\right] d x \\ =x \sqrt{x^{2}+a^{2}}-\int\left[\frac{1}{2 \sqrt{x^{2}+a^{2}}}(2 x) \cdot x\right] d x \\ =x \sqrt{x^{2}+a^{2}}-\int \frac{\left(x^{2}+a^{2}-a^{2}\right.}{\sqrt{x^{2}+a^{2}}} d x . \\ \text { – }=x \sqrt{x^{2}+a^{2}}-\int \frac{x^{2}+a^{2}}{\sqrt{x^{2}+a^{2}}} d x+a^{2} \int \frac{d x}{\sqrt{x^{2}+a^{2}}} \\ \therefore I=x \sqrt{x^{2}+a^{2}}-\int \sqrt{x^{2}+a^{2}} d x+a^{2} \int \frac{d x}{\sqrt{x^{2}+a^{2}}} \text {. } \\ {\left[\because \int \frac{d x}{\sqrt{x^{2}+a^{2}}}=\log \left|x+\sqrt{x^{2}+a^{2}}\right|+c .\right]} \\ \end{array}$

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Question 2

Three of the following four are alike in a certain way based on the information given above and so form a group. Which is does not belong to that group?

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Question 4

41% [ الس. * * * 6:38 PM | 0.0KB/s C. Crop Image X No.: Date: Q. Change the order of integration & evaluate. y = √2-x²0x² x=1 I dx dy | x² + y²

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 Question Text Class: subject: hence evaluate (i) or (ii)) $\begin{array}{l} \therefore I=\sqrt{x^{2}+a^{2}} \int 1 d x-\int\left[\frac{d\left(\sqrt{x^{2}+a^{2}}\right)}{d x} \cdot \int 1 d x\right] d x \\ =x \sqrt{x^{2}+a^{2}}-\int\left[\frac{1}{2 \sqrt{x^{2}+a^{2}}}(2 x) \cdot x\right] d x \\ =x \sqrt{x^{2}+a^{2}}-\int \frac{\left(x^{2}+a^{2}-a^{2}\right.}{\sqrt{x^{2}+a^{2}}} d x . \\ \text { – }=x \sqrt{x^{2}+a^{2}}-\int \frac{x^{2}+a^{2}}{\sqrt{x^{2}+a^{2}}} d x+a^{2} \int \frac{d x}{\sqrt{x^{2}+a^{2}}} \\ \therefore I=x \sqrt{x^{2}+a^{2}}-\int \sqrt{x^{2}+a^{2}} d x+a^{2} \int \frac{d x}{\sqrt{x^{2}+a^{2}}} \text {. } \\ {\left[\because \int \frac{d x}{\sqrt{x^{2}+a^{2}}}=\log \left|x+\sqrt{x^{2}+a^{2}}\right|+c .\right]} \\ \end{array}$ Updated On Jan 13, 2023 Topic Calculus Subject Mathematics Class Class 12 Passed Answer Type Video solution: 1 Upvotes 113 Avg. Video Duration 8 min

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