Integral Calculator

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Example

Created on 2024-06-20Asked by Chloe Taylor (Solvelet student)

Evaluate the integral

\int (3x^2 + 2x + 1) \, dx

Solution

To evaluate the integral

\int (3x^2 + 2x + 1) \, dx

: Integrate each term separately:

\int 3x^2 \, dx + \int 2x \, dx + \int 1 \, dx

Use the power rule for integration:

\int x^n \, dx = \frac{x^{n+1}}{n+1} + C

Apply the power rule to each term:

\int 3x^2 \, dx = 3 \cdot \frac{x^3}{3} = x^3

\int 2x \, dx = 2 \cdot \frac{x^2}{2} = x^2

\int 1 \, dx = x

Combine the results:

\int (3x^2 + 2x + 1) \, dx = x^3 + x^2 + x + C

Therefore, the integral

\int (3x^2 + 2x + 1) \, dx

is:

\int (3x^2 + 2x + 1) \, dx = x^3 + x^2 + x + C

Where

C

is the constant of integration. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Chloe Thomas on Solvelet

1. Evaluate the integral

\int_0^1 (3x^2 + 2x + 1) \, dx

,2. Evaluate the integral

\int \frac{x^2 + 3x - 2}{(x - 1)(x + 2)} \, dx

using partial fraction decomposition.,

DefinitionIntegration is a mathematical technique that simply collects the quantities, for example areas under curve, total distance covered, accumulated quantities in an interval. The two chief types are the definite integral, which represents a number, and the indefinite integral, which represents a function (the antiderivative of the given function). Calculus is the study of integrals and is essential for solving physics, engineering, economics ans many other problems. Where The definite integral ∫abf(x)dx denotes the area between curve f(x) from x=a to x=b.

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