TS EAMCET · Maths · Indefinite Integration
If \(\int \frac{x}{(a+x)^5} d x=\frac{1}{k(a+x)^4}(f(x))+c\) then \(\frac{f(-a)}{a k}=\)
- A \(\frac{1}{3}\)
- B \(\frac{1}{2}\)
- C \(\frac{5}{6}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } u=x+a \\ & d u=d x \\ & \int \frac{u-a}{u^5} d u=\int \frac{1}{u^4} d u-\int \frac{a}{u^5} d u \\ & =\frac{1}{3 u^3}+\frac{a}{4 u^4}+C=\frac{-4 u+3 a}{12 u^4}+C=\frac{-4(x+a)+3 a}{12(x+a)^4}+C \\ & =\frac{1}{12(x+a)^4}(-4 x-a)+C \\ & f(x)=-4 x-a…
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
- Given that \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n p} f\left(\frac{r}{n}\right)=\int_0^p f(x) d x\). If \(f: \mathbb{R} \rightarrow \mathbb{R}\) is defined by \(f(x)=x^2+2\), then \[ \lim _{n \rightarrow \infty} \frac{3}{n}\left[f\left(\frac{7}{n}\right)+f\left(\frac{14}{n}\right)+f\left(\frac{21}{n}\right)+\ldots+f(7)\right]= \]TS EAMCET 2022 Hard
- If two equal sides of an isosceles triangle are given by the equations \(7 x-y+3=0\) and \(x+y-3=0\), then the equation of its third side passing through the point \((2,-5)\) isTS EAMCET 2020 Medium
- \(f(x)\) is a twrice differentiable function such that \(f^{\prime \prime}(x)=-f(x)\) and \(f^{\prime}(x)=g(x)\). If \(\left.h(x)=(f(x))^2+g(x)\right)^2\) and \(h(l)=2\), then \(h(2)=\)TS EAMCET 2019 Easy
- If the solution for the differential equation \(y^2 d x+\left(x^2-x y-y^2\right)\) \(d y=0\) at \((2,1)\) is \(x+y=k\left(x y^2-y^3\right)\), then \(\mathrm{k}=\)TS EAMCET 2023 Medium
- A student is allowed to select at least \((n+1)\) books but not all books from a collection of \((2 n+1)\) books. If the total number of ways in which he can select these books is 255, then the number of books in that collection isTS EAMCET 2020 Easy
- The mid-point of a chord of the ellipse \(x^2+4 y^2-2 x+20 y=0 \quad\) is \((2,-4)\). The equation of the chord isTS EAMCET 2013 Medium
More PYQs from TS EAMCET
- The negative feedback in an amplifierTS EAMCET 2025 Easy
- The dihedral angles in gaseous and solid phases of \(\mathrm{H}_2 \mathrm{O}_2\) molecule respectively areTS EAMCET 2024 Medium
- Consider the curves and Assertion : The common tangents to the curves and are orthogonal. Reason : and are the common tangents to the curves andTS EAMCET 2019 Medium
- In which of the following reactions hydrogen is not liberated?TS EAMCET 2011 Medium
- The height of a cone with semi vertical angle \(\pi / 3\) is increasing at the rate of 2 units \(/ \mathrm{min}\). The rate at which the radius of the cone is to be decreased so as to have a fixed volume always isTS EAMCET 2025 Medium
- If the direction cosines of two lines are given by \(l+m+n=0\) and \(l^2-5 m^2+n^2=0\), then the angle between them isTS EAMCET 2014 Medium