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sinx+x^2
Solving integrals/ sinx+x^2

Integral of sinx+x^2 dx

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The solution

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∫01(x2+sin⁡(x)) dx\int\limits_{0}^{1} \left(x^{2} + \sin{\left(x \right)}\right)\, dx 
Integral(sin(x) + x^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    1. The integral of sine is negative cosine:

      ∫sin⁡(x) dx=−cos⁡(x)\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}

    The result is: x33−cos⁡(x)\frac{x^{3}}{3} - \cos{\left(x \right)}

  2. Add the constant of integration:

    x33−cos⁡(x)+constant\frac{x^{3}}{3} - \cos{\left(x \right)}+ \mathrm{constant}

The answer is:

x33−cos⁡(x)+constant\frac{x^{3}}{3} - \cos{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \sin(x) + x / dx = C - cos(x) + --
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∫(x2+sin⁡(x)) dx=C+x33−cos⁡(x)\int \left(x^{2} + \sin{\left(x \right)}\right)\, dx = C + \frac{x^{3}}{3} - \cos{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
4/3 - cos(1)
43−cos⁡(1)\frac{4}{3} - \cos{\left(1 \right)} 
=
= 
4/3 - cos(1)
43−cos⁡(1)\frac{4}{3} - \cos{\left(1 \right)} 
4/3 - cos(1)
Numerical answer [src] 
0.793031027465194
0.793031027465194
The graph
Integral of sinx+x^2 dx

    Use the examples entering the upper and lower limits of integration.

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