What is the integral from 0 to 5 of ti+t^2j+t^3k ?

The integral from 0 to 5 of ti+t^2j+t^3k is (5t^3k+5t^2j)+5it

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integral from 0 to 5 of ti+t^2j+t^3k

\int_{0}^{5} t i + t^{2} j + t^{3} k d x

(5 t^{3} k + 5 t^{2} j) + 5 i t

Solution steps

\int_{0}^{5} t i + t^{2} j + t^{3} k d x

Integral of a constant:

\int a d x = a x

= [(t^{2} j + t^{3} k + t i) x]_{0}^{5}

Compute the boundaries:

(5 t^{3} k + 5 t^{2} j) + 5 i t

= 5 t^{3} k + 5 t^{2} j + 5 i t

Simplify

= (5 t^{3} k + 5 t^{2} j) + 5 i t

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\int_{0}^{0.5} e^{- x^{3}} d x

What is the integral from 0 to 5 of ti+t^2j+t^3k ?
The integral from 0 to 5 of ti+t^2j+t^3k is (5t^3k+5t^2j)+5it