Math, asked by Anonymous, 1 month ago

Find the area under the curve f(x) = 4x - x² from x = 0, and x = 4.​

Answers

Answered by sahaabhilasha4
3

Step-by-step explanation:

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Answered by Anonymous
1

Step-by-step explanation:

f(x) = 4x -  {x}^{2}

Area under the curve is given by,

 \displaystyle \implies \int \limits^{4}_0f(x)  \: dx

 \displaystyle \implies \int \limits^{4}_04x -  {x}^{2}   \: dx

 \displaystyle \implies \int \limits^{4}_04x \: dx -  {\int \limits^{4}_0}   {x}^{2}  \: dx

 \displaystyle \implies4\int \limits^{4}_0x \: dx - \left  [\frac{{x}^{3} }{3} \right]^4_0

 \displaystyle \implies4 \left[\frac{ {x}^{2} }{2} \right]^4_0 -    \left  [\frac{{x}^{3} }{3} \right]^4_0

{ \displaystyle \implies 4\left[\frac{ {4}^{2} }{2} -  \frac{ {0}^{2} }{2}  \right]-    \left  [\frac{{4}^{3} }{3} -  \frac{ {0}^{3} }{3}  \right]}

{ \displaystyle \implies 4\left[\frac{16}{2} \right]-    \left  [\frac{64 }{3}  \right]}

{ \displaystyle \implies 32-  \frac{64 }{3}}

{ \displaystyle \implies \frac{96 - 64 }{3}}

 \boxed { \displaystyle \implies \frac{32}{3}}

Therefore the area under the curve is 32/3 square units.

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