MHT CET · Maths · Indefinite Integration
\(\int \mathrm{e}^x \cos x \mathrm{~d} x=\)
- A \(\frac{\mathrm{e}^x \cos x}{2}+\sin x+\mathrm{c}, \quad\) where c is the constant of integration.
- B \(\frac{\mathrm{e}^x(\sin x+\cos x)}{2}+\mathrm{c}, \quad\) where c is the constant of integration.
- C \(\mathrm{e}^x\left(\frac{\cos x-\sin x}{2}\right)+\mathrm{c}, \quad\) where c is the constant of integration.
- D \(\mathrm{e}^x\left(\frac{\sin x-\cos x}{2}\right)+\mathrm{c}, \quad\) where c is the constant of integration.
Answer & Solution
Correct Answer
(B) \(\frac{\mathrm{e}^x(\sin x+\cos x)}{2}+\mathrm{c}, \quad\) where c is the constant of integration.
Step-by-step Solution
Detailed explanation
\(I = \int \mathrm{e}^x \cos x \mathrm{~d} x\) Using integration by parts: \(\int u \mathrm{~d} v = u v - \int v \mathrm{~d} u\)
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
- The area of the region bounded by the curve \(y=\log x, x\) -axis and the lines
\(x=1, x=e\) isMHT CET 2020 Medium - The length of the perpendicular to the plane \(\bar{r} \cdot(\hat{\imath}-2 \hat{\jmath}+3 \hat{k})=14\) from the origin isMHT CET 2020 Easy
- If \((2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0\) and \(y(0)=1\), then \(y\left(\frac{\pi}{2}\right)\) isMHT CET 2023 Medium
- The equation of the plane through the line of intersection of \(\overline{\mathrm{r}} \cdot(2 \hat{i}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})=1\) and \(\overline{\mathrm{r}} \cdot(\hat{i}-\hat{\mathrm{j}})+4=0\) and perpandicular to \(\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})+8=0\) is \(\bar{r} \cdot(-5 \hat{i}+2 \hat{j}+12 \hat{k})=\mu\). Then \(\mu=\)MHT CET 2025 Medium
- The probability that bomb will miss the target is \(0 \cdot 2\). Then the probability that out of 10 bombs dropped exactly 2 will hit the target isMHT CET 2020 Easy
- The principal solutions of the equation \(\sec x+\tan x=2 \cos x\) areMHT CET 2023 Easy
More PYQs from MHT CET
- The co-ordinates of the points on the line \(2 x-y=5\) which are the distance of 1 unit from the line \(3 x+4 y=5\) areMHT CET 2023 Medium
- In an extrinsic n-type semiconductor, the free electrons donated by the impurity atoms occupy energy levels inMHT CET 2024 Easy
- The apparent wavelength of light from a star moving away from the earth is \(0.02 \%\) more than the actual wavelength. The velocity of star is \(\left[\mathrm{c}=\right.\) velocity of light \(\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right]\)MHT CET 2025 Medium
- The surface of water in a water tank of cross section area \(750 \mathrm{~cm}^2\) on the top of a house is ' \(h\) ' \(m\) above the tap level. The speed of water coming out through the tap of cross section area \(500 \mathrm{~mm}^2\) is \(30 \mathrm{~cm} / \mathrm{s}\). At that instant \(\frac{\mathrm{dh}}{\mathrm{dt}}\) is \(\mathrm{x}=10^{-3} \mathrm{~m} / \mathrm{s}\). The value of ' x ' will beMHT CET 2024 Medium
- Which from following statements about rate constant is NOT true?MHT CET 2023 Easy
-
The values taken by \(C, D, E, F\) are respectivelyMHT CET 2022 Easy