MHT CET · Maths · Inverse Trigonometric Functions
\(\int_1^3\left[\tan ^{-1}\left(\frac{x}{x^2-1}\right)+\tan ^{-1}\left(\frac{x^2-1}{x}\right)\right] d x=\)
- A \(\pi\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(2 \pi\)
Answer & Solution
Correct Answer
(A) \(\pi\)
Step-by-step Solution
Detailed explanation
\(\text { Let } I=\int_1^3\left[\tan ^1\left(\frac{x}{x^2-1}\right)+\tan ^{-1}\left(\frac{x^2-1}{x}\right)\right]\) \(d x \)
\( \int_1^3\left[\tan ^{-1}\left(\frac{x}{x^2-1}\right)+\cot ^{-1}\left(\frac{x}{x^2-1}\right)\right] d x \)
\( =\int_1^3\left(\frac{\pi}{2}\right) d x=\frac{\pi}{2} \int_1^3 d x=\frac{\pi}{2}[x]_1^3=\pi\)
\( \int_1^3\left[\tan ^{-1}\left(\frac{x}{x^2-1}\right)+\cot ^{-1}\left(\frac{x}{x^2-1}\right)\right] d x \)
\( =\int_1^3\left(\frac{\pi}{2}\right) d x=\frac{\pi}{2} \int_1^3 d x=\frac{\pi}{2}[x]_1^3=\pi\)
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 the line through the points \((-2,6)\) and \((4,8)\) is perpendicular to the line passing through the points \((8,12)\) and \((x, 24)\), then the value of \(x\) isMHT CET 2022 Easy
- The curve \(y=\mathrm{a} x^3+\mathrm{b} x^2+\mathrm{c} x+5\) touches the x -axis at \((-2,0)\) and cuts the \(y\)-axis at a point Q where its gradient is 3 , then the value of \(\mathrm{a}+\mathrm{b}+\mathrm{c}\) isMHT CET 2024 Medium
- The Cartesian equation of the line which passes through the points \((3,1,2)\) and \((-1,2,1)\) isMHT CET 2022 Easy
- If area of the parallelogram with \(\bar{a}\) and \(\bar{b}\) as two adjacent sides is 20 square units, then the area of the parallelogram having \(3 \bar{a}\) \(+\overline{\mathrm{b}}\) and \(2 \overline{\mathrm{a}}+3 \overline{\mathrm{b}}\) as two adjacent sides in square units isMHT CET 2021 Easy
- The equations of two ellipses are be \(\frac{x^2}{4}+\frac{y^2}{2}=1\) and \(\frac{x^2}{36}+\frac{y^2}{b^2}=1\). If the product of their eccentricities is \(\frac{\sqrt{2}}{3}\), then the product of the length of the major axis and minor axis of the second ellipse is \(\qquad\)MHT CET 2025 Medium
- If \(y=\left((x+1)(4 x+1)(9 x+1) \ldots\left(\mathrm{n}^2 x+1\right)\right)^2\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(x=0\) isMHT CET 2024 Easy
More PYQs from MHT CET
- If the lines \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-1}{4}\) and \(\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}\) intersect, then k has the valueMHT CET 2024 Medium
- Which of the following is NOT involved in the formation of secondary rainbow?MHT CET 2023 Easy
- When \(\mathrm{SO}_{2}\) is passed through acidified \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{0}\), the process that takes place isMHT CET 2020 Medium
- If \(\bar{a}=\hat{i}+\hat{j}, \overline{\mathrm{~b}}=2 \hat{i}-\hat{\mathrm{k}}\) then the point of intersection of the lines \(\overline{\mathrm{r}} \times \overline{\mathrm{a}}=\overline{\mathrm{b}} \times \overline{\mathrm{a}}\) and \(\overline{\mathrm{r}} \times \overline{\mathrm{b}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) isMHT CET 2025 Easy
- The equation of wave motion is \(\mathrm{Y}=5 \sin (10 \pi \mathrm{t}\) \(-0.02 \pi x+\pi / 3)\) where \(x\) is in metre and \(t\) in second. The velocity of the wave isMHT CET 2023 Medium
- If foci of the ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1\left(b^{2} < 16\right)\) and the hyperbola \(\frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25}\) coincide,
then the value of \(b^{2}\) isMHT CET 2020 Easy