Question

integration of (x+3) (2-x)​

Answer 1

Answer:

x = -3 & x = 2

Step-by-step explanation:

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Answer 2

${ \bold{ \mathscr{\boxed{INTEGRATION}}}}$

${\rm \bold{\int(x + 3)(2 - x)}} \: dx \\ \\ \implies \int2x - x {}^{2} + 6 - 3x \: \: dx\\ \\ \implies \int \: 6 - x { - x \: }^{2} \: dx$

[ Multiplying the terms ]

→ Now , separating the integral we get

$\int6 \: \: dx \: \: - \int \: x \: \: dx \: - \int \: x {}^{2} \: dx \\ \\ \implies6x \: - \frac{x {}^{1 + 1} }{1 + 1} - \frac{x {}^{2 + 1} }{2 + 1} + c\\ \: \\ \implies \: 6x \: - \dfrac{{x}^{2} }{2} - \frac{x {}^{3} }{3} + c$

So the solution of the given integral is

$\huge\int( x + 3)(2 - x) \: = 6x - \frac{x {}^{2} }{2} - \frac{x {}^{3} }{3} + c$

Where C is any Arbitrary Constant .