AP EAMCET · Maths · Indefinite Integration
\(\int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x=\)
- A \(e^x+c\)
- B \(\frac{-2}{1-2 x}+c\)
- C \(2 e^{2 x}+c\)
- D \(\frac{\mathrm{e}^{2 \mathrm{x}}}{2}+\mathrm{c}\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{e}^{2 \mathrm{x}}}{2}+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!} = \sum_{r=0}^{\infty} \frac{(2x)^r}{r!} = e^{2x}\) \(\int e^{2x} d x = \frac{e^{2x}}{2} + c\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int_2^5 \sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}} d x=\)AP EAMCET 2022 Medium
- Let \(\mathbf{u}, \mathbf{v}\) and \(\mathbf{w}\) be three vectors such that \(\mathbf{u}+\mathbf{v}+\mathbf{w}=0,|\mathbf{u}|=3,|\mathbf{v}|=5\) and \(|\mathbf{w}|=7\). Then the angle between \(\mathbf{u}\) and \(\mathbf{v}\) isAP EAMCET 2020 Easy
- In \(\triangle A B C, b c-r_2 r_3=\)AP EAMCET 2024 Medium
- The solution of the differential equation isAP EAMCET 2021 Hard
- If \(\alpha, \beta\) and \(\gamma\) are length of the altitudes of a \(\triangle A B C\) with area \(\Delta\), then \(\frac{\Delta^2}{R^2}\left(\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}\right)\) is equal toAP EAMCET 2012 Medium
- If \(\log (x+y)-2 x y=0\), then \(y^{\prime}(0)=\)AP EAMCET 2020 Easy
More PYQs from AP EAMCET
- If \(\tanh ^2 x=\tan ^2 \theta\) then \(\cosh 2 x=\)AP EAMCET 2017 Medium
- A man of \(50 \mathrm{~kg}\) is standing at one end on a boat of length \(25 \mathrm{~m}\) and mass \(200 \mathrm{~kg}\). If he starts running and when he reaches the other end, he has a velocity \(2 \mathrm{~ms}^{-1}\) with respect to the boat. The final velocity of the boat is : (in \(\mathrm{ms}^{-1}\) )AP EAMCET 2006 Easy
- \(\sin A+\sin B=\sqrt{3}(\cos B-\cos A)\)
\(\Rightarrow \sin 3 A+\sin 3 B\) is equal toAP EAMCET 2007 Hard - The number of radial nodes, angular nodes of a orbital are respectivelyAP EAMCET 2022 Medium
- RMS velocity of one mole of an ideal gas was measured at different temperatures. A graph of \(\left(\mathrm{u}_{\mathrm{rms}}\right)^2\) (on y -axis) and \(\mathrm{T}(\mathrm{K})\) (on x -axis) gave straight line passing through the origin and its slope is \(249 \mathrm{~m}^2 \mathrm{~s}^{-2} \mathrm{~K}^{-1}\). What is the molar mass (in \(\left.\mathrm{kg} \mathrm{mol}^{-1}\right)\) of ideal gas? \(\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)\)AP EAMCET 2024 Hard
- A straight line \(\mathrm{L}\) at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular drawn from the origin to this line makes an angle of \(60^{\circ}\) with the line \(x+y=0\). Then the equation of the line \(\mathrm{L}\) isAP EAMCET 2023 Medium