Here are some good Integrals class 12 important questions for Mathematics. Solutions Related Articles find the range of a function

Integration of even function over a symmetric intervalcan be simplified as follows: $\int_{-a}^{a} f(x) \, dx = 2 \int_{0}^{a} f(x) \, dx$ This simplification is possible because the area under the curve from $-a$ to $0$ is the same as the area from $0$ to $a$ due to the symmetry of the function. Example 1$\int_{-a}^{a}

Integration of sin x cos x dx can be found using various integration technique like integration by substitution, Integration by partial fraction along with trigonometric identities. The various formula for integration of sin x cos x dx are I \[\int \sin(x) \cos (x)\, dx = -\frac {1}{4} \cos (2x) + C\] II \[\int \sin(x) \cos

For integration of $\log(\sin x)$, we generally consider the definite integral over the interval from 0 to $\pi/2$ To calculate the definite integral of $\log(\sin x)$ from (0) to $\pi/2$, we use a technique involving symmetry and the properties of logarithms. The integral is: \[\int_{0}^{\pi/2} \log(\sin x) \, dx\] Let $I=\int_{0}^{\pi/2} \log(\sin x) \, dx$