MathDB
Today's calculation of Integral 362

Source: 2008 Miyazaki University entrance exam/Agriculture

July 19, 2008
calculusintegrationtrigonometrylogarithmscalculus computations

Problem Statement

Evaluate the following definite integrals. (1) 0π2xcosx dx \int_0^{\frac{\pi}{2}} x\cos x\ dx. (2) \int_1^2 \frac{1}{x(x\plus{}1)}\ dx. (3) \int_0^1 \frac{1}{1\plus{}e^x}\ dx. (4) 0π4cos2xcos3x dx \int_0^{\frac{\pi}{4}} \cos 2x \cos 3x \ dx.