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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^2*exp(x^3)
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Integral of 1/(2x-1)
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Integral of x(x^2+1)^3
- Integral of e^(1/x)
- Canonical form:
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y^2+x^2
- The double integral of:
- y^2+x^2
- y^2+x^2
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Identical expressions
- y^ two +x^ two
- y squared plus x squared
- y to the power of two plus x to the power of two
- y2+x2
- y²+x²
- y to the power of 2+x to the power of 2
- y^2+x^2dx
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Similar expressions
- xy^2+(x^2)/8
- y^2-x^2
Integral of y^2+x^2 dx
The solution
You have entered
[src]
___ \/ 5 / | | / 2 2\ | \y + x / dx | / 1
$$\int\limits_{1}^{\sqrt{5}} \left(x^{2} + y^{2}\right)\, dx$$
Integral(y^2 + x^2, (x, 1, sqrt(5)))
Detail solution
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Integrate term-by-term:
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The integral of is when :
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The integral of a constant is the constant times the variable of integration:
The result is:
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Now simplify:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | 3 | / 2 2\ x 2 | \y + x / dx = C + -- + x*y | 3 /
$$\int \left(x^{2} + y^{2}\right)\, dx = C + \frac{x^{3}}{3} + x y^{2}$$
The answer
[src]
___ 1 2 5*\/ 5 ___ 2 - - - y + ------- + \/ 5 *y 3 3
$$- y^{2} + \sqrt{5} y^{2} - \frac{1}{3} + \frac{5 \sqrt{5}}{3}$$
=
=
___ 1 2 5*\/ 5 ___ 2 - - - y + ------- + \/ 5 *y 3 3
$$- y^{2} + \sqrt{5} y^{2} - \frac{1}{3} + \frac{5 \sqrt{5}}{3}$$
-1/3 - y^2 + 5*sqrt(5)/3 + sqrt(5)*y^2
Use the examples entering the upper and lower limits of integration.