Let $I_n={\int }_0^{\frac{1}{2}}\frac{1}{\sqrt{1-x^n}}dx$ where $n>2$, then

Important Questions on Definite Integration

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JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 50

If $f\left(x\right)=2^{\left\{x\right\}}$, Where $\left\{x\right\}$ denotes the fractional part of $x$. Then which of the following is true?

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 51

Let $f\left(x\right)={\int }_0^x\left|2t-3\right|dt,$ then $f$ is

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 52

Let $I_n={\int }_0^{\pi }{\left(\sin x\right)}^{n}dx, n\in N,$ then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 53

Let $f\left(x\right)$ be a function satisfying $f\left(x\right)+f\left(x+2\right)=10\forall x\in R,$ then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 54

Let $I_n={\int }_0^{\pi }\frac{{\sin }^2\left(nx\right)}{{\sin }^{2}x}dx, n\in N,$ then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 55

Let $f\left(x\right)$ be a continuous function and $I={\int }_1^9\sqrt{x}f\left(x\right)dx,$ then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 56

Let $A={\int }_1^{e^2}\frac{\ln x}{\sqrt{x}}dx$, then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 30 - Definite Integration>Exercise-2>Q 57

Let $f\left(a,b\right)={\int }_a^b\left(x^2-4x+3\right)dx,\left(b>a\right)$, then