AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}} d x=\frac{3}{2}(\tan x)^B+\frac{1}{10}(\tan x)^A+c\) then \(\mathrm{A}=\)
- A \(\frac{1}{2}\)
- B \(1\)
- C \(5\)
- D \(\frac{5}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}}=\frac{3}{2 \cos ^3 x \sqrt{\frac{4 \tan x}{1+\tan ^2 x}}}\) \(I=\int \frac{3 \sec ^4 x}{4 \sqrt{\tan x}} d x=\int \frac{3}{4} \frac{\left(1+\tan ^2 x\right)}{\sqrt{\tan x}} \sec ^2 x d x\)…
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
- If \(A=\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right)\) where \(\theta=\frac{2 \pi}{19}\) then \(\mathrm{A}^{2017}=\)AP EAMCET 2017 Hard
- Given that the solid obtained by rotating a rectangle about one of its side is a cylinder. If the perimeter of a rectangle is \(48 \mathrm{~cm}\) and the volume of the cylinder formed by rotating it is maximum, then the dimensions of that rectangle isAP EAMCET 2023 Hard
- The point \((a, b)\) is the foot of the perpendicular drawn from the point \((3,1)\) to the line \(x+3 y+4=0\). If \((p, q)\) is the image of \((a, b)\) with respect to the line \(3 x-4 y+11=\) 0 , then \(\frac{p}{a}+\frac{q}{b}=\)AP EAMCET 2024 Hard
- Find the equation of the circle which passes through the point and the points of intersection of the circles and .AP EAMCET 2021 Medium
- If \(f(0)=0, f(1)=1, f(2)=2\) and \(f(x)=f(x-2)+f(x\) \(-3)\) for \(x=3,4,5 \ldots\), then \(f(10)=\)AP EAMCET 2023 Easy
- Find the equation of normal to the curve \(y=x^3-3 x\), which is parallel to the line \(2 x+18 y=9\) ?AP EAMCET 2020 Medium
More PYQs from AP EAMCET
- Consider the following statements:
I. In diamond, each carbon atom is \(s p^3\)-hybridised.
II. Graphite has planar hexagonal layers of carbon atoms.
III. Silicones being surrounded by non-polar alkyl groups are water repelling in nature
IV. The order of catenation in group 14 elements is \(\mathrm{Si}>\mathrm{C}>\mathrm{Sn}>\mathrm{Ge}>\mathrm{Pb}\).
The correct statements areAP EAMCET 2019 Hard - For \(\mathrm{NaCl}\), the number of Schottky pairs per \(\mathrm{cm}^3\) at room temperature isAP EAMCET 2021 Medium
- \(1+\frac{1}{3}+\frac{1.3}{3.6}+\frac{1.3 .5}{3.6 .9}+\ldots\) to \(\infty=\)AP EAMCET 2024 Medium
- If \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\vec{b}=2 \hat{i}-3 \hat{j}-5 \hat{k}\), thenAP EAMCET 2023 Easy
- Assertion (A) The colour of radiation does not change on passing through different media.
Reason (R) The media do not absorb or emit colours.AP EAMCET 2021 Medium - The artificial sweetener X contains glycosidic linkage and Y contains amide, ester linkages. X and Y respectively areAP EAMCET 2025 Medium