Maths

we can have three integration of 1 sinx cosx ( integration of 1 /sinx+ cosx , integration of 1 /sinx- cosx and integration of 1 /sinx cosx). Here are formula of these integrals (I) integration of 1 /sinx+ cosx $\int \frac {1}{sinx + cos x} \; dx = \frac {1}{\sqrt{2}} \log \left| \frac {\left(\tan\left(\frac{x}{2}\right) – […]

The integral of the root x, can be found using power rule. The integral of $\sqrt x $ with respect to (x) is: \[\int \sqrt x \, dx =\frac{2}{3} x^{3/2} + C\] Here, (C) represents the constant of integration, which is added because the process of integration determines the antiderivative up to an arbitrary constant.

This article is about surds questions and follow the link surds in math if you want to know about surds. Here in this article, you can find surds problem-solving questions. Surd Easy Questions Simplify the following Answers (1) $\sqrt{21} \times \sqrt{7}= \sqrt { 3 \times 7 \times 7} = 7 \sqrt 3$(2) $\sqrt{180} = \sqrt

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 $I=\int_{0}^{\pi/2} \log(\sin x) \, dx$

Number 30 is a composite number and we will find how to find the factors of 30. We will also see techniques to find out the Prime factorization of 30 easily Factors of 30 A factor of a number is an exact divisor of that number. So factors of 30 are the numbers which are