What is the integral of (3t^2i+4tj-8t^3k) ?

The integral of (3t^2i+4tj-8t^3k) is it^3+2jt^2-2kt^4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3t^2i+4tj-8t^3k)

\int (3 t^{2} i + 4 t j - 8 t^{3} k) d t

i t^{3} + 2 j t^{2} - 2 k t^{4} + C

Solution steps

\int 3 t^{2} i + 4 t j - 8 t^{3} k d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 t^{2} i d t + \int 4 t j d t - \int 8 t^{3} k d t

\int 3 t^{2} i d t = i t^{3}

\int 4 t j d t = 2 j t^{2}

\int 8 t^{3} k d t = 2 k t^{4}

= i t^{3} + 2 j t^{2} - 2 k t^{4}

Add a constant to the solution

= i t^{3} + 2 j t^{2} - 2 k t^{4} + C

\int (4 cos (x)) d x

\int \frac{2 x ^{2} + 3}{x ^{2} 4 - x ^{2}} d x

2 x^{- 1}

\int \frac{x + 2}{7 - 9 x ^{2}} d x

\int sin^{4} (x) x d x

What is the integral of (3t^2i+4tj-8t^3k) ?
The integral of (3t^2i+4tj-8t^3k) is it^3+2jt^2-2kt^4+C