1
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-1
Change Language

Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $$\int\limits_{ - 6}^0 {f(x)dx} $$ is equal to __________.

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2
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-1
Change Language

The value of the integral

$${{48} \over {{\pi ^4}}}\int\limits_0^\pi {\left( {{{3\pi {x^2}} \over 2} - {x^3}} \right){{\sin x} \over {1 + {{\cos }^2}x}}dx} $$ is equal to __________.

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3
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1
Change Language

The value of b > 3 for which $$12\int\limits_3^b {{1 \over {({x^2} - 1)({x^2} - 4)}}dx = {{\log }_e}\left( {{{49} \over {40}}} \right)} $$, is equal to ___________.

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4
JEE Main 2022 (Online) 24th June Evening Shift
Numerical
+4
-1
Change Language

The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is __________.

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