MHT CET · Maths · Indefinite Integration
\(\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots . .+a^{n-1}\right) d x=\) (where \(C\) is a constant of integration)
- A \(\frac{x^{n+1}}{n+1}-a^n x+C\)
- B \(x^n-a^n+C\)
- C \(\frac{x^{n+1}}{n+1}-a^n+C\)
- D \(n a^{n-1}+C\)
Answer & Solution
Correct Answer
(A) \(\frac{x^{n+1}}{n+1}-a^n x+C\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \int(x-a)\left(x^{n-1}+x^{n-2} \cdot a+\ldots \ldots+a^{n-1}\right) d x \\ & =\int\left(x^n-a^n\right) d x \\ & =\frac{x^{n+1}}{n+1}-a^n x+c\end{aligned}\)
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
- In a \(\triangle \mathrm{PQR}, \mathrm{m} \angle \mathrm{R}=\frac{\pi}{2}\). If \(\tan \left(\frac{\mathrm{P}}{2}\right)\) and \(\tan \left(\frac{\mathrm{Q}}{2}\right)\) are the roots of the equation \(a x^2+b x+c=0(a \neq 0)\), thenMHT CET 2024 Medium
- The position of a point in time t is given by \(x=\mathrm{a}+\mathrm{bt}-\mathrm{ct}^2, \mathrm{y}=\mathrm{at}+\mathrm{bt}^2\).
It's resultant acceleration at time \(t\) in seconds is given byMHT CET 2025 Medium - If \(\bar{a}, \overline{\mathrm{~b}}, \overline{\mathrm{c}}\) are three coplanar vectors such that \(|\bar{a}|=1,|\overline{\mathrm{~b}}|=2, \overline{\mathrm{~b}} \cdot \overline{\mathrm{c}}=8\) and the angle between \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) is \(45^{\circ}\) then the value of \(|\bar{a} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})|\) isMHT CET 2025 Medium
- The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, isMHT CET 2024 Easy
- If 6 boys and 3 girls are to be seated on chairs for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side isMHT CET 2025 Easy
- Let \(\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]\) and \(\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I}_2\), (where \(\mathrm{I}_2\) is unit matrix of order 2), thenMHT CET 2024 Hard
More PYQs from MHT CET
- Which among the following carbohydrate molecules yields highest number of galactose molecules when one mole of each is hydrolyzed?MHT CET 2022 Easy
- Calculate the work done during combustion of 0.138 kg of ethanol, \(\left( C _2 H _5 OH ( l )\right)\) at at 300 K . Given: \(R=8.314 Jk ^{-1} mol^{-1}\) and molar mass of ethanol \(=46 g~ mol ^{-1}\).MHT CET 2018 Hard
- The ratio of the total energy of the \(2^{\text {nd }}\) orbit electron for the hydrogen atom \(1 \mathrm{H}^1\) to that of helium ion \(\left(\mathrm{He}^{+}\right) 2 \mathrm{He}^4\) isMHT CET 2025 Medium
- If \(\bar{a}, \bar{b}, \bar{c}\) are three vectors which are perpendicular to \(\overline{\mathrm{b}}+\overline{\mathrm{c}}, \overline{\mathrm{c}}+\overline{\mathrm{a}}\), and \(\overline{\mathrm{a}}+\overline{\mathrm{b}}\) respectively, such that \(|\overline{\mathrm{a}}|=2|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4\), then \(|\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}|=\)MHT CET 2021 Medium
- The length of latus rectum of the parabola whose focus is at \((1,-2)\) and directrix is
the line \(x+y+3=0\) isMHT CET 2020 Medium - Lacteals are present in the mucosa of__________.MHT CET 2024 Easy