Antiderivatives Calculator

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Example

Created on 2024-06-20Asked by Mateo Brown (Solvelet student)

Find the antiderivative of

f(x) = \sin(x)

Solution

Step 1: Identify the function to integrate. The function is

f(x) = \sin(x).

Step 2: Find the antiderivative. The antiderivative of

\sin(x)

is:

\int \sin(x) \, dx = -\cos(x) + C,

where

C

is the constant of integration. Step 3: Conclusion. The antiderivative of

f(x) = \sin(x)

-\cos(x) + C

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Some of the related questions asked by Henry Mitchell on Solvelet

1. Determine the antiderivative of the function

f(x) = 3x^2 - 2x + 5

2. Evaluate the integral

\int_{0}^{2} (4x^3 - 2x) \, dx

DefinitionAn Antiderivative of a Function f(x) is defined as another function F(x)whose derivative is equal to f(x). In terms of integral calculus, F(x)is the antiderivative of f(x), that helps to find the area under the curves defined by f(x). For example, an antiderivative of function f(x)=2xf (x) =2xf(x)=2x is going to be F(x)=x2+C F(x) =x2+C F(x)=x2+C, where C is the constant of integration and it represents solutions.

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