Question

What is ∫6x2 dx ????

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\int\,6\,x^2\;dx}$

$\underline{\textbf{To find:}}$

$\textsf{Integral of}\;\mathsf{6\,x^2}$

$\underline{\textbf{Solution:}}$

$\mathsf{\int\,6\,x^2\;dx}$

$\textsf{Take the constant 6 outside the integral}$

$\textsf{by using the property of integral}$

$\;\boxed{\mathsf{\int\,k\,f(x)\;dx=k\,\int\,\,f(x)\;dx}}$

$\mathsf{=6\int\,x^2\;dx}$

$\textsf{Using the formula}$

$\boxed{\mathsf{\int\,x^n\,dx=\dfrac{x^{n+1}}{n+1}+C}}$

$\mathsf{=6\left(\dfrac{x^3}{3}\right)+C}$

$\mathsf{=2(x^3)+C}$

$\mathsf{=2\,x^3+C}$

$\implies\boxed{\bf\int\,6\,x^2\;dx=2\,x^3+C}$

Answer 2

Step-by-step explanation:

We have,

$\displaystyle \sf \int 6x^2 dx$

$\displaystyle \sf 6\int x^2 dx$

We know that,

• $\underline{\boxed{ \displaystyle \bf{\int x^n = \dfrac{x^{(n+1)}}{(n+1)} }}} \pink \bigstar$

$= \displaystyle \sf 6 \bigg( \dfrac{x^3}{3} \bigg) + c$

$\displaystyle \bf{\int 6 {x}^{2} =} \bf {2x^3 +c}$