Download App

STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
$\int\limits_{ - \,1}^1 {\,\,\frac{{{x^3}\, + \,\,|x|\,\, + \,\,1}}{{{x^2}\, + \,\,2\,|x|\,\, + \,\,1}}}\,dx$ $= a\, ln\, 2 + b$ then :
  • A
    $a = 2 ; b = 1$
  • ✓
    $a = 2 ; b = 0$
  • C
    $a = 3 ; b = - 2$
  • D
    $a = 4 ; b = - 1$
✓

Answer

Correct option: B.
$a = 2 ; b = 0$
b
$I =\int\limits_{ - \,1}^1 {\,\,\frac{{{x^3}}}{{{x^2}\,\, + \,\,2\,\left| x \right|\,\, + \,\,1}}} $  $dx +\int\limits_{ - \,1}^1 {\,\,\frac{{\left| x \right|\,\, + \,\,1}}{{{{\left( {\left| x \right|\,\, + \,\,1} \right)}^2}}}} dx $

$\,\Rightarrow 2 \int\limits_0^1 {\,\,\frac{{dx}}{{1\,\, + \,\,x}}} = 2\, ln \,2$
odd $\Rightarrow$ vanishes even 

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $f (x)$ be diffrentiable at $x = h$ then $\mathop {\lim }\limits_{x \to h} \,\frac{{(x + h)\,f(x)\, - 2h\,f(h)}}{{x - h}}$ is equal to
→
If $\text{f(x)}=\begin{cases}\text{ax}^2+\text{b},&0\leq\text{x}<1\\4,&\text{x}=1\\\text{x}+3,&1<\text{x}\leq2\end{cases}$ then the value of (a, b) for which f(x) cannot be continuous at x = 1, is:
→
Let $f(x) = x^2$ and $g(x) = 2^x.$ Then, the solution set of the equation $fog(x) = gof(x)$ is:
→
$\int\limits^3_0\frac{3\text{x}+1}{\text{x}^2+9}\text{ dx}=$
→
If A and B are two matrices of order 3×m and 3×n respectively and m = n, then the order of 5A - 2B is:
→
Let the probability of getting head for a biased coin be $\frac{1}{4}$. It is tossed repeatedly until a head appears. Let $N$ be the number of tosses required. If the probability that the equation $64 x ^2+5 Nx +1=0$ has no real root is $\frac{ p }{ q }$, where $p$ and $q$ are co-prime, then $q-p$ is equal to
→
Let $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in R$ Then $f^{\prime}(10)$ is equal to ..............
→
The value of $\int\limits^\frac{\pi}{4}_0\cos\text{x}\text{ e}^{\sin\text{x}}\text{ dx}$ is :
→
If $f(x) = |x - 3|,$ then $f$ is
→
The range of values of the function $f\left( x \right) = \frac{1}{{2 - 3\sin x}}$ is
→