_ 1 ^ 6 ([sec^ -1 ]+[cot^ -1 ])dx is equal to (where [.] denotes … - Vidyadip

MCQ

$\int_{1}^{6\pi}([sec^{-1}]+[cot^{-1}])dx$ is equal to (where $[.]$ denotes greatest integer function)

A
$12\pi-sec1$
B
$6\pi-cot1$
C
$6\pi-cot1-sec1$
✓
$6\pi-sec1$

✓

Answer

Correct option: D.

$6\pi-sec1$

d
$\int\limits_1^{6\pi } {\left( {\left[ {{{\sec }^{ - 1}}x} \right] + \left[ {{{\cot }^{ - 1}}x} \right]} \right)} dx$

$ = \int\limits_1^{6\pi } {\left[ {{{\sec }^{ - 1}}x} \right]} + \int\limits_1^{6\pi } {\left[ {{{\cot }^{ - 1}}x} \right]dx} $

$ = \int\limits_1^{\sec 1} {0.dx} + \int\limits_{\sec 1}^{6\pi } {1.dx + 0 = } 6\pi - \sec 1$

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 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area enclosed by the curve $y = (x - 1) (x - 2) (x - 3)$ between the co-ordinate axes and the ordinate at $x = 3$ is :

$\int_{}^{} {{x^{51}}({{\tan }^{ - 1}}x + {{\cot }^{ - 1}}x)\;dx = } $

Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^5-5 x+a$. Then

$(A)$ $f(x)$ has three real roots if $a > 4$

$(B)$ $f(x)$ has only one real root if $a > 4$

$(C)$ $f(x)$ has three real roots if $a < -4$

$(D)$ $f ( x$ ) has three real roots if $-4 < a < 4$

Find the minor of $a_{22}$ of the matrix
$
\left[\begin{array}{lll}
1 & 6 & 1 \\
5 & 3 & 0 \\
2 & 2 & 9
\end{array}\right] \text {. }
$

Solution of the differential equation $xdy = (y + xy^3 (1 + log_ex))\ dx$ is (Where $C$ is arbitary constant)

If $f(x) \, \& \,g(x)$ are inverse functions of each other such that $f(1) = 3\, \& \,f(3) = 1,$ then $\int\limits_1^3 {\left( {g(x) + \frac{x}{{f'\left( {g\left( x \right)} \right)}}} \right)} dx$ is equal to -

$\int_{}^{} {\frac{{dx}}{{4{{\cos }^3}2x - 3\cos 2x}}} = $

The angle between the pair of lines with direction ratios $(1, 1, 2)$ and $(\sqrt 3 - 1, - \sqrt 3 - 1,4)$ is ......... $^o$

Let the position vectors of points $A$ and $B$ be $\hat{ i }+\hat{ j }+\hat{ k }$ and $2 \hat{ i }+\hat{ j }+3 \hat{ k },$ respectively. A point $P$ divides the line segment $AB$ internally in the ratio $\lambda: 1(\lambda>0) .$ If $O$ is the origin and $\overline{ OB } \cdot \overrightarrow{ OP }-3|\overrightarrow{ OA } \times \overrightarrow{ OP }|^{2}=6,$ then $\lambda$ is equal to

The value of the integral $\int \limits_{-\pi / 2}^{\pi / 2} \frac{\sin ^2 x}{1+e^x}\,d x$ is