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Question
\int _{2}^{4}\left(y^{2}-3y+5\right) dy
Evaluate the integral
\frac{32}{3}
Alternative Form
10\frac{2}{3}
Alternative Form
10.\dot{6}
Evaluate
\int _{2}^{4}\left(y^{2}-3y+5\right) dy
Evaluate the integral
\int \left(y^{2}-3y+5\right) dy
\text{Use the property of integral }\int f(x) \pm g(x) dx=\int f(x) dx \pm \int g(x) dx
\int y^{2} dy+\int -3y dy+\int 5 dy
Evaluate the integral
More Steps
Evaluate
\int y^{2} dy
\text{Use the property of integral }\int x^{n} dx = \frac{x^{n+1}}{n+1}
\frac{y^{2+1}}{2+1}
Add the numbers
\frac{y^{3}}{2+1}
Add the numbers
\frac{y^{3}}{3}
\frac{y^{3}}{3}+\int -3y dy+\int 5 dy
Evaluate the integral
More Steps
Evaluate
\int -3y dy
\text{Use the property of integral }\int kf(x) dx=k\int f(x) dx
-3\times \int y dy
\text{Use the property of integral }\int x^{n} dx = \frac{x^{n+1}}{n+1}
-3\times \frac{y^{1+1}}{1+1}
Add the numbers
-3\times \frac{y^{2}}{1+1}
Add the numbers
-3\times \frac{y^{2}}{2}
Multiply the terms
-\frac{3y^{2}}{2}
\frac{y^{3}}{3}-\frac{3y^{2}}{2}+\int 5 dy
\text{Use the property of integral }\int k dx = kx
\frac{y^{3}}{3}-\frac{3y^{2}}{2}+5y
Return the limits
\left(\frac{y^{3}}{3}-\frac{3y^{2}}{2}+5y\right)\bigg |_{2}^{4}
Solution
More Steps
Substitute the values into formula
\frac{4^{3}}{3}-\frac{3\times 4^{2}}{2}+5\times 4-\left(\frac{2^{3}}{3}-\frac{3\times 2^{2}}{2}+5\times 2\right)
Multiply the terms
More Steps
Evaluate
3\times 2^{2}
Evaluate the power
3\times 4
Multiply the numbers
12
\frac{4^{3}}{3}-\frac{3\times 4^{2}}{2}+5\times 4-\left(\frac{2^{3}}{3}-\frac{12}{2}+5\times 2\right)
Multiply the terms
More Steps
Evaluate
3\times 4^{2}
Evaluate the power
3\times 16
Multiply the numbers
48
\frac{4^{3}}{3}-\frac{48}{2}+5\times 4-\left(\frac{2^{3}}{3}-\frac{12}{2}+5\times 2\right)
Divide the terms
More Steps
Evaluate
\frac{12}{2}
Reduce the numbers
\frac{6}{1}
Calculate
6
\frac{4^{3}}{3}-\frac{48}{2}+5\times 4-\left(\frac{2^{3}}{3}-6+5\times 2\right)
Multiply the numbers
\frac{4^{3}}{3}-\frac{48}{2}+5\times 4-\left(\frac{2^{3}}{3}-6+10\right)
Divide the terms
More Steps
Evaluate
\frac{48}{2}
Reduce the numbers
\frac{24}{1}
Calculate
24
\frac{4^{3}}{3}-24+5\times 4-\left(\frac{2^{3}}{3}-6+10\right)
Multiply the numbers
\frac{4^{3}}{3}-24+20-\left(\frac{2^{3}}{3}-6+10\right)
Calculate the sum or difference
More Steps
Evaluate
\frac{2^{3}}{3}-6+10
Evaluate the power
\frac{8}{3}-6+10
Add the numbers
\frac{8}{3}+4
\text{Write all numerators above the least common denominator }3
\frac{8}{3}+\frac{4\times 3}{1\times 3}
Calculate
\frac{8}{3}+\frac{12}{3}
Add the terms
\frac{8+12}{3}
Add the terms
\frac{20}{3}
\frac{4^{3}}{3}-24+20-\frac{20}{3}
Evaluate the power
\frac{64}{3}-24+20-\frac{20}{3}
Add the numbers
\frac{64}{3}-4-\frac{20}{3}
Subtract the numbers
More Steps
Evaluate
\frac{64}{3}-\frac{20}{3}
Subtract the terms
\frac{64-20}{3}
Subtract the terms
\frac{44}{3}
\frac{44}{3}-4
\text{Write all numerators above the least common denominator }3
\frac{44}{3}-\frac{4\times 3}{1\times 3}
Calculate
\frac{44}{3}-\frac{12}{3}
Subtract the terms
\frac{44-12}{3}
Subtract the terms
\frac{32}{3}
\frac{32}{3}
Alternative Form
10\frac{2}{3}
Alternative Form
10.\dot{6}
Show Solutions
