promath The integral of $\sqrt{1-x^2}$ is equal to $\dfrac{x}{2} \sqrt{1-x^2}$ $+\dfrac{1}{2}$ sin-1 x+C. Here we will learn how to integrate square root of 1-x2. The integral formula of root 1-x^2 is provided below:$\int \sqrt{1-x^2} dx$ $=\dfrac{x}{2} \sqrt{1-x^2}$ $+\dfrac{1}{2}$ sin-1 x+C. Integration of $\sqrt{1-x^2}$ Question: How to Integrate Root (1-x^2)? That is, find $\int \sqrt{1-x^2} dx$. Solution: … Read more
The integral of root tanx is equal to ∫√tanx dx = $\dfrac{1}{\sqrt{2}}$ tan-1 ($\dfrac{\tan x-1}{\sqrt{2\tan x}}$) + $\dfrac{1}{2\sqrt{2}}$ log $|\dfrac{\tan x+1-\sqrt{2\tan x}}{\tan x+1+\sqrt{2\tan x}}|$ +C where C denotes an integral constant. In this post, we will learn how to find the integral of square root of tanx. Integration of √tanx Question: Find ∫√tanx dx. Solution: … Read more
The derivative of ln(1/x) is equal to -1/x, where ln denotes the logarithm with base e, that is, ln(x)=logex. In this post, we will find the derivative of ln(1/x). Note that ln(1/x) is the natural logarithm of 1/x. Its derivative formula is given below: $\dfrac{d}{dx}\big( \ln (\dfrac{1}{x}) \big)=-\dfrac{1}{x}$. Derivative of ln(1/x) by Chain Rule Let … Read more
The derivative of root 1-x^2 is equal to -x/√(1-x2). Here we differentiate square root of 1-x2 by chain rule and implicit differentiation method. Note that $\dfrac{d}{dx} \Big( \sqrt{1-x^2}\Big)=-\dfrac{x}{\sqrt{1-x^2}}$. Let us now differentiate root 1-x2. Derivative of root 1-x2 by Chain Rule Question: Find the derivative of square root 1-x2. Answer: Let us put z = … Read more
The Laplace transform of delta function is equal to L{δ(t)} = 1. Here we find the Laplace of Dirac delta function, that is, unit impulse function. The Dirac delta function is also known as the unit impulse function. Its Laplace transform formula is given by L{δ(t)} = 1. Laplace Transform of Dirac Delta Function Recall … Read more
The Laplace transform of unit step function is equal to 1/s. The unit step function, denoted by, u(t), is defined as follows: $u(t) = \begin{cases} 0, & \text{if } t<0 \\ 1, & \text{if } t \geq 0. \end{cases}$ The Laplace transform of u(t), unit step function, is given by L{u(t)} = $\dfrac{1}{s}$. Laplace transform … Read more
The Laplace transform of e^t is equal to L{et} = 1/(s-1) whenever s>1. Here we find the Laplace of et by the definition of Laplace transforms. The formula of the Laplace of et is given by L{et} = $\dfrac{1}{s-1}$. Find the Laplace Transform of et By definition of Laplace transforms, the Laplace transform of a … Read more
Answer: The Laplace transform of 0 is equal to L{0} = 0. In this post, we learn to find the Laplace of zero. The formula of the Laplace transform of zero is given as follows: L{0} = 0. Laplace Transform of 0 By definition, the Laplace of f(t) is given by the integral L{f(t)} = … Read more
The Laplace transform of t is equal to L{t} = 1/s2. Here we will find the Laplace of t by the definition of Laplace transforms. The formula of the Laplace of t is given as follows: L{t} = $\dfrac{1}{s^2}$. Find Laplace Transform of t Recall, the definition of the Laplace transform. According to this, the … Read more
The Laplace transform of sin t is equal to 1/(s2+1), and it is denoted by L{sint}. Here we will find the Laplace of sint by the definition of Laplace transforms. The formula of the Laplace of sint is given by L{sint} = $\dfrac{1}{s^2+1}$. Laplace transform of sint By definition, the Laplace transform of f(t) is … Read more