TS EAMCET · Maths · Indefinite Integration
If \(\int \mathrm{e}^x\left(\sin ^2 2 \mathrm{x}-8 \cos 4 \mathrm{x}\right) \mathrm{dx}=\mathrm{e}^x f(\mathrm{x})+\mathrm{c}\), then \(f\left(\frac{\pi}{4}\right)=\)
- A \(0\)
- B \(1\)
- C \(-1\)
- D \(e\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int e^x\left(\sin ^2 2 x-8 \cos 4 x\right) d x \\ & =\int e^x\left(\frac{1-\cos 4 x}{2}-8 \cos 4 x\right) d x \\ & =\int e^x\left(\frac{1-17 \cos 4 x}{2}\right) d x \\ & =\frac{1}{2}\left[\int e^x d x-17 \int e^x \cos 4 x d x\right] \\ & \because \int e^{a x}…
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 length (in units) of the common chord of the circles and is:TS EAMCET 2021 Easy
- The most general value of \(\theta\) which satisfies both the equations \(\tan 8=-1\) and \(\cos \theta=\frac{1}{\sqrt{2}}\) isTS EAMCET 2011 Medium
- In a data with 15 number of observations \(x_1\), \(x_2, x_3, \ldots, x_{15}, \sum_{i=1}^{15} x_i^2=3600\) and \(\sum_{i=1}^{15} x_i=175\). If the value of one observation 20 was found wrong and was replaced by its correct value 40 , then the corrected variance of that data isTS EAMCET 2019 Medium
- For the ellipse \(4 x^2+y^2-8 x+2 y+1=0\), the focus and the equation of the directrix are respectivelyTS EAMCET 2018 Medium
- A circle of radius 4 , drawn on a chord of the parabola \(y^2=8 x\) as diameter, touches the axis of the parabola. Then, the slope of the chord isTS EAMCET 2013 Hard
- For any \(n \in N, 4^n+15 n-1\) is divisible byTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- The half-life of \(\mathrm{Ra}^{226}\) is 1620 years. Then the number of atoms decay in one second in \(1 \mathrm{~g}\) of radium (Avogadro number \(=6.023 \times 10^{23}\) )TS EAMCET 2012 Medium
- If \(\frac{d y}{d x}=4\) and \(\frac{d^2 y}{d x^2}=-3\) at a point \(P\) on the curve \(y=f(x)\), then \(\left(\frac{d^2 x}{d y^2}\right)_p=\)TS EAMCET 2019 Easy
- The IUPAC name of the following compound isTS EAMCET 2023 Easy
- The centre of the circle passing through the point \((0,1)\) and touching the curve \(y=x^2\) at \((2,4)\) isTS EAMCET 2019 Medium
- Two blocks of masses \(2 \mathrm{~kg}\) and \(1 \mathrm{~kg}\) are tied to the ends of a string which passes over a light frictionless pulley. The blocks are held at rest at the same horizontal level and then released suddenly. The distance traversed by their centre of mass in 2 seconds is (acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )TS EAMCET 2023 Medium
- At \(27^{\circ} \mathrm{C}\), a closed vessel contains a mixture of equal weights of helium (mol. wt. =4), methane (mol, wt. =16) and sulphur dioxide (mol. wt. = 64). The pressure exerted by the mixture is \(210 \mathrm{~mm}\). If the partial pressures of helium, methane and sulphur dioxide are \(p_1, p_1\) and \(p_3\) respectively, which one of the following is correct?TS EAMCET 2002 Easy