Question 1 :
The area of the region bounded by the {tex} x {/tex} -axis and the curves defined by {tex} y = \tan x , ( - \pi / 3 \leq x \leq \pi / 3 ) {/tex} is

Question 2 :
If {tex} f ( x ) = f ( a - x ) , {/tex} then {tex} \int\limits _ { 0 } ^ { a } x f ( x ) d x {/tex} equals

Question 3 :
Value of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870e0375ed294f2c7c4508' height='37' width='63' >(b - x)⁴ dx is

Question 4 :
The value of &lambda; for which <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e74c4b99a86374798f06ca0' height='40' width='72' >dx = log (4^x + x⁴) is -

Question 5 :
The area of the region bounded by y = e^x, y = e^-x, x = 0 and x = 1 is

Question 6 :
If the area above the {tex} x {/tex} -axis, bounded by the curves {tex} y = 2 ^ { k x } {/tex} and {tex} x = 0 {/tex} and {tex} x = 2 {/tex} is {tex} \frac { 3 } { \ln 2 } {/tex}, then the value of {tex} k {/tex} is

Question 7 :
The area enclosed between the curve y = log_e(x + e) and the coordinate axes is

Question 9 :
Area of region satisfying x &le; 2, y &le; |x| and x &ge; 0 is-

Question 10 :
The area bounded by y = ln x, the x-axis and the ordinates x = 0 and x = 1, is

Question 11 :
Let {tex} f ( x ) {/tex} be a non-negative continuous function such that the area bounded by the curve {tex} y = f ( x ) {/tex}, {tex} x {/tex} -axis and the ordinates {tex} x = \frac { \pi } { 4 } {/tex} and {tex} x = \beta > \frac { \pi } { 4 } {/tex} is {tex} \left( \beta \sin \beta + \frac { \pi } { 4 } \cos \beta + \sqrt { 2 } \beta \right) . {/tex} Then {tex} f \left( \frac { \pi } { 2 } \right) {/tex} is

Question 12 :
The parabolas {tex} y ^ { 2 } = 4 x {/tex} and {tex} x ^ { 2 } = 4 y {/tex} divide the square region bounded by the lines {tex} x = 4 , y = 4 {/tex} and the coordinate axes. If {tex} S _ { 1 } , S _ { 2 } , S _ { 3 } {/tex} are respectively the areas of these parts numbered from top to bottom; then {tex} S _ { 1 }: S _ { 2 }: S _ { 3 } {/tex} is

Question 13 :
{tex} \int \left\{ \frac { ( \log x - 1 ) } { 1 + ( \log x ) ^ { 2 } } \right\} ^ { 2 } d x {/tex} is equal to

Question 14 :
{tex} \int \limits_ { 0 } ^ { \pi } x f ( \sin x ) d x {/tex} is equal to

Question 15 :
{tex} {\underset{ n \rightarrow \infty }{lim}} \left[ \frac { 1 } { n ^ { 2 } } \sec ^ { 2 } \frac { 1 } { n ^ { 2 } } + \frac { 2 } { n ^ { 2 } } \sec ^ { 2 } \frac { 4 } { n ^ { 2 } } + \ldots + \frac { 1 } { n } \sec ^ { 2 } 1 \right] {/tex} equals

Question 16 :
If ∫₀^x²f(t) dt = xcos πx, then the value of f(4) is

Question 17 :
If I₁ = ∫₀¹2^x² dx, I₂ = ∫₀¹2^x³ dx, I₃ = ∫₁²2^x² dx and I₄ = ∫₁²2^x³ dx, then

Question 18 :
The area bounded by the curves y = |x| − 1 and y = − |x| + 1 is

Question 20 :
{tex} \int \frac { d x } { \cos x - \sin x } {/tex} is equal to