Set the limits of integration in ∫∫
The teacher will be very surprised to see your correct solution to the integral 😉
What can it do?
- Plot the region of integration D
- Previously, you define this region using equations of curves and inequalities
- Finds points of intersection between the lines in this region, thus determining points for limits
- Based on the resulting contour, the limits of integration and their order in the integral are defined
Examples of how to set the limits of integration in a double integral
The above examples also contain:
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the modulus or absolute value: absolute(x) or |x|
-
square roots sqrt(x),
cubic roots cbrt(x)
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trigonometric functions:
sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
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exponential functions and exponents exp(x)
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inverse trigonometric functions:
arcsine asin(x), arccosine acos(x), arctangent atan(x),
arccotangent acot(x)
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natural logarithms ln(x),
decimal logarithms log(x)
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hyperbolic functions:
hyperbolic sine sh(x), hyperbolic cosine ch(x),
hyperbolic tangent and cotangent tanh(x), ctanh(x)
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inverse hyperbolic functions:
hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x),
hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
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other trigonometry and hyperbolic functions:
secant sec(x), cosecant csc(x), arcsecant asec(x),
arccosecant acsc(x), hyperbolic secant sech(x),
hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x),
hyperbolic arccosecant acsch(x)
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rounding functions:
round down floor(x), round up ceiling(x)
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the sign of a number:
sign(x)
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for probability theory:
the error function erf(x) (integral of probability),
Laplace function laplace(x)
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Factorial of x:
x! or factorial(x)
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Gamma function gamma(x)
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Lambert's function LambertW(x)
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Trigonometric integrals: Si(x),
Ci(x),
Shi(x),
Chi(x)
The insertion rules
The following operations can be performed
- 2*x
- - multiplication
- 3/x
- - division
- x^2
- - squaring
- x^3
- - cubing
- x^5
- - raising to the power
- x + 7
- - addition
- x - 6
- - subtraction
- Real numbers
- insert as 7.5, no 7,5
Constants
- pi
- - number Pi
- e
- - the base of natural logarithm
- i
- - complex number
- oo
- - symbol of infinity
Use the examples entering the upper and lower limits of integration in the double integral.