It has two types-definite integral and indefinite integral. It is used to obtain the area, volume and displacement, etc. Integral is the result of the integration. For example, the integral of {eq}\sin{x} {/eq} is {eq}-\cos{x}+C {/eq}, where {eq}C {/eq} is the integral con...
The substitution of some variable in the place of trigonometric ratios is known as the trigonometric substitution. We will use the trigonometric integral to evaluate the integral of the given function.Answer and Explanation: Given: I=∫cot(x) dxI=∫cos(x)sin(x) dx Let......
What is the exact value of {eq}\int_0^4 e^x \,dx {/eq}? Definite Integral: The definite integral of a function {eq}f(x) {/eq} over the interval {eq}[a,b] {/eq} {eq}\displaystyle \int_{a}^{b} f(x) \; dx {/eq} ...
What is L Hospital Rule Formula? The formula of L Hopitals rule is limx → af(x) / g(x) = limx → af' (x) / g'(x), where the left side limit gives an indeterminate form by applying the limit x = a. Here f'(x) and g'(x) are the derivatives of the respectivefunctions...
The integral is the measure of the area under the curve of the function. It accumulates the discrete values of a function over a range of values. Calculus is also referred to as infinitesimal calculus or “the calculus of infinitesimals”. Infinitesimal numbers are quantities that have a value...
If ∫16f(x)dx=−10 and ∫36f(x)dx=−8, then what is the value of ∫13f(x)dx ? Definite Integrals: The indefinite integrals that are evaluated with the upper and lower limits are known as Definite integrals. Suppose, we have a definite integral ∫abf...
Q: Why is the integral/antiderivative the area under a function? Thank you! Mathematical proof of the existence of God. Video: Getting Computers to Learn Q: What is going on in a nuclear reactor, and what happens during a meltdown? Q: How do I find the love of my life? (a Mathem...
and instead of a summation you have an integral, but the essential idea is the same. Here, is the honest-to-god actual Fourier transform of f. Now here’s a big part of why mathematicians love Fourier transforms so much that they want to have billions of their babies, naming them in...
What is the integral of cos^2(3x) dx? What is the integral of 1/(2x) dx? What's the integral of sec(x)tan(x) dx? If f(x) = integral e^x dx and f (0) = 2, then what is f(2)? a) e^2. b) e^2 - 1. c) e^2 + 1. d) e + 2. ...
What is the integral of sec(x)(sec(x) + tan(x))? Integrals- Formulas and Explanation: In mathematics, the integral of a function indicates the approximate area enclosed by the curve of a function. The sign of integration is {eq}\int {/eq}, and if the lower and upper limit of the...