নির্দিষ্ট যোগজীকরণ (Definite Integration)

অনুশীলনী \(10.G\) উদাহরণ সমুহ
নিচের যোগজগুলির মান নির্ণয় করঃ
\((1.)\) \(\int_{1}^{2}{\frac{(x^2-1)^2}{x^2}dx}\)
উত্তরঃ \(\frac{5}{6}\)

\((2.)\) \(\int_{0}^{\frac{\pi}{2}}{\cos^2{x}dx}\)
উত্তরঃ \(\frac{\pi}{4}\)

\((3.)\) \(\int_{1}^{3}{\frac{2x}{1+x^2}dx}\)
উত্তরঃ \(\ln{5}\)

\((4.)\) \(\int_{1}^{3}{\frac{1}{x}\cos{(\ln{|x|})}dx}\)
উত্তরঃ \(\sin{(\ln{3})}\)

\((5.)\) \(\int_{0}^{1}{\frac{1}{\sqrt{2x-x^2}}dx}\)
উত্তরঃ \(\frac{\pi}{2}\)

\((6.)\) \(\int_{0}^{1}{\ln{|1+x|}dx}\)
উত্তরঃ \(2\ln{2}-1\)

\((7.)\) \(\int_{0}^{\frac{\pi}{2}}{e^x(\sin{x}+\cos{x})dx}\)
উত্তরঃ \(e^{\frac{\pi}{2}}\)
\((8.)\) \(\int_{0}^{4}{y\sqrt{4-y}dx}\)
উত্তরঃ \(\frac{128}{15}\)

\((9.)\) \(\int_{0}^{3}{(3-2x+x^2)dx}\)
উত্তরঃ \(9\)

\((10.)\) \(\int_{0}^{\frac{\pi}{2}}{\frac{\sin{x}}{\sin{x}+\cos{x}}dx}\)
উত্তরঃ \(\frac{\pi}{4}\)

\((11.)\) \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}{|\sin{x}|dx}\)
উত্তরঃ \(2\)

\((12.)\) \(\int_{2}^{8}{|x-5|dx}\)
উত্তরঃ \(9\)

\((13.)\) \(\int_{0}^{3}{\sqrt{9-x^2}dx}\)
উত্তরঃ \(\frac{9\pi}{4}\)
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