find the avarage value of the function on the given interval
f(x)=xe-2,[0,5]
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Calculus Examples
Popular Problems
Calculus
Find the Average Value of the Function f(x)=e^x , [0,5]
f(x)=exf(x)=ex , [0,5][0,5]
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(−∞,∞)(-∞,∞)
Set-Builder Notation:
{x|x∈R}{x|x∈ℝ}
f(x)f(x) is continuous on [0,5][0,5].
f(x)f(x) is continuous
The average value of function ff over the interval [a,b][a,b] is defined as A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx.
A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx
Substitute the actual values into the formula for the average value of a function.
A(x)=15−0(∫50exdx)A(x)=15-0(∫05exdx)
The integral of exex with respect to xx is exex.
A(x)=15−0(ex]50)A(x)=15-0(ex]05)
Substitute and simplify.
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A(x)=15−0(e5−1)A(x)=15-0(e5-1)
Simplify the denominator.
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A(x)=
Enter a problem...
Calculus Examples
Popular Problems
Calculus
Find the Average Value of the Function f(x)=e^x , [0,5]
f(x)=exf(x)=ex , [0,5][0,5]
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(−∞,∞)(-∞,∞)
Set-Builder Notation:
{x|x∈R}{x|x∈ℝ}
f(x)f(x) is continuous on [0,5][0,5].
f(x)f(x) is continuous
The average value of function ff over the interval [a,b][a,b] is defined as A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx.
A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx
Substitute the actual values into the formula for the average value of a function.
A(x)=15−0(∫50exdx)A(x)=15-0(∫05exdx)
The integral of exex with respect to xx is exex.
A(x)=15−0(ex]50)A(x)=15-0(ex]05)
Substitute and simplify.
Tap for more steps...
A(x)=15−0(e5−1)A(x)=15-0(e5-1)
Simplify the denominator.
Tap for more steps...
A(x)=
Calculus Examples
Popular Problems
Calculus
Find the Average Value of the Function f(x)=e^x , [0,5]
f(x)=exf(x)=ex , [0,5][0,5]
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(−∞,∞)(-∞,∞)
Set-Builder Notation:
{x|x∈R}{x|x∈ℝ}
f(x)f(x) is continuous on [0,5][0,5].
f(x)f(x) is continuous
The average value of function ff over the interval [a,b][a,b] is defined as A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx.
A(x)=1b−a∫baf(x)dxA(x)=1b-a∫abf(x)dx
Substitute the actual values into the formula for the average value of a function.
A(x)=15−0(∫50exdx)A(x)=15-0(∫05exdx)
The integral of exex with respect to xx is exex.
A(x)=15−0(ex]50)A(x)=15-0(ex]05)
Substitute and simplify.
Tap for more steps...
A(x)=15−0(e5−1)A(x)=15-0(e5-1)
Simplify the denominator.
Tap for more steps...
A(x)=