Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Choose the correct answer in Exercise:
The value of $\int^{1}_{0}\tan^{-1}\bigg(\frac{2\text{x}-1}{1+\text{x}-\text{x}^{2}}\bigg)\text{dx}$ is
  • A
    1
  • ✓
    0
  • C
    -1
  • D
    $\frac{\pi}{4}$
✓

Answer

Correct option: B.
0
$\text{Let I}=\int^{1}\limits_{0}\tan^{-1}\bigg(\frac{2\text{x}-1}{1+\text{x}-\text{x}^{2}}\bigg)\text{dx}$

$\Rightarrow\text{I}=\int^{1}\limits_{0}\tan^{-1}\bigg(\frac{\text{x}-(1-\text{x})}{1+\text{x}(1-\text{x})}\bigg)\text{dx}$

$\Rightarrow\text{I}=\int^{1}\limits_{0}\Big[\tan^{-1}\text{x}-\tan^{-1}(1-\text{x)}\Big]\text{dx}$

$\Rightarrow\text{I}=\int^{\text{1}}\limits_{0}\Big[\tan^{-1}(1-\text{x)}-\tan^{-1}(1-1+\text{x)}\Big]\text{dx}$

$\Rightarrow\text{I}=\int^{1}\limits_{0}\Big[\tan^{-1}(1-\text{x)}-\tan^{-1}\text{(x)}\Big]\text{dx}$

$\Rightarrow\text{I}=\int^{1}_{0}\Big[\tan^{-1}(1-\text{x)}-\tan^{-1}\text{(x)}\Big]\text{dx}$

Adding (1) and (2), we obtain

$\Rightarrow2\text{I}=\int^{1}\limits_{0}\Big(\tan^{-1}\text{x)}+\tan^{-1}(1-\text{x)}-\tan^{-1}\text{x}\Big)\text{dx}$

$\Rightarrow2\text{I}=0$

$\Rightarrow\text{I}=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\int\limits^\pi_{-\pi}\sin^3\text{x}\cos^2\text{x}\text{ dx}$ is:
→
$\cos^{-1}\Big(\frac{1}{2}\Big)$
→
If $|\vec{a}|=3,|\vec{b}|=4$ and $|\vec{a}+\vec{b}|=5$, then $|\vec{a}-\vec{b}|=$
→
${x^x}$ has a stationary point at
→
If matrix $A = \left[ {\begin{array}{*{20}{c}}
{\sin \theta }&{\cos ec\theta }&1\\
{\cos ec\theta }&1&{\sin \theta }\\
1&{\sin \theta }&{\cos ec\theta }
\end{array}} \right]$ is a non invertible matrix, then possible value of $'\theta'$ is 

$($ where $n \in I)$

→
If six cards are selected at random $($without replacement$)$ from a standard deck of $52$ cards, what is the probability that there will be no pairs? $($two cards of same denomination$)$
→
The figure formed by the four points $i + j - k,\,\,\,2i + 3j,$ $3i + 5j - 2k$ and $k - j$ is
→
Choose the correct answer from the given four option.The differential equation for $\text{y}=\text{A}\cos\alpha\text{x}+\text{B}\sin\alpha\text{x},$ where $A$ and $B$ are arbitrary constants is:
→
Let $f(x + y) = f(x)f(y)$ and $f(x) = 1 + \sin (3x)g(x)$ where $g(x)$ is continuous then $f'(x)$ is
→
The relation 'R' in N × N such that (a, b)R(c, d) ⇔ a + d = b + c is:
→