JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Indefinite Integrals

More JEE Main questions on Indefinite Integrals

1. If …
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2. Let $f(x)=\int \frac{\left(2-x^2\right)\cdot e^x}{(\sqrt{1+x})(1-x{)}^{3/2}}dx$. If $f(0)=0$, then $\mathrm{f}\left(\frac{1}{2}\right)$ is equal to :
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3. Let $\mathrm{I}(\mathrm{x})=\int \frac{3\mathrm{dx}}{(4\mathrm{x}+6)\left(\sqrt{4{\mathrm{x}}^2+8\mathrm{x}+3}\right)}$ and $\mathrm{I}(0)=\frac{\sqrt{3}}{4}+20$. If $\mathrm{I}\left(\frac{1}{2}\right)=\frac{\mathrm{a}\sqrt{2}}{\mathrm{b}}+\mathrm{c}$, where …
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4. Let $\mathrm{f}(\mathrm{t})=\int \left(\frac{1-\sin \left({\log }_{\mathrm{e}}\mathrm{t}\right)}{1-\cos \left({\log }_{\mathrm{e}}\mathrm{t}\right)}\right)\mathrm{dt},\mathrm{t}>1$.
   
   If $\mathrm{f}\left({\mathrm{e}}^{\pi /2}\right)=-{\mathrm{e}}^{\pi /2}$ and …
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5. Let $f(x)=\int \frac{7x^{10}+9x^8}{{\left(1+x^2+2x^9\right)}^2}dx,x>0$,
   ${\lim }_{x\to 0}f(x)=0$ and $f(1)=\frac{1}{4}$. …
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6. If $\int \left(\frac{1-5{\cos }^{2}x}{{\sin }^{5}x{\cos }^{2}x}\right)dx=f(x)+C$ where $C$ is the constant of integration, then $\mathrm{f}\left(\frac{\pi }{6}\right)-\mathrm{f}\left(\frac{\pi }{4}\right)$ is equal to
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