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3 years ago

It's a ven dyagram question pls help

Mathematics

1 answer:

slamgirl [31]3 years ago

5 0

Answer:

a) A U B = {21,23,24,25,27,29,30,31 }

b) A n C = {24,30}

Step-by-step explanation:

A {21,24,27,30}

B {21,23,25,27,29,31}

C {20,22,24,26,28,30,32}

a) A U B = {21,23,24,25,27,29,30,31 }

b) A n C = {24,30}

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sashaice [31]

Answer:

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Step-by-step explanation:

Given that:

$f ''(x)= 6x +sinx$

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We will have to integrate it twice to find the value of f(x).

Let us have a look at the basic formula of integration that we will use in the solution:

$1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C$

$\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\$

Now, integrating it again to find f(x):

$f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D$

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klasskru [66]

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