Mathematics: Compute the integral (a) int sin (pi x) dx by letting u = pi x. (b) int e^(x/2) dx by letting u = x/2. Show that you got the correct answer by differentiating the computed function.

Compute the integral (a) int sin (pi x) dx by

Ответ:

whitakers87

20.01.2022

Mathematics

(a) $\int sin(\pi x) dx$ $=-\frac {cos \pi x}{\pi}+c$

(b) $\int e^\frac{x}{2} dx$ $=2e^\frac{x}{2}+c$

Step-by-step explanation:

(a)

$\int sin(\pi x) dx$

Let u = π x

differentiating with respect to x

du = π dx

$\Rightarrow dx=\frac{du}{\pi}$

Putting the value of x and dx

$=\int sin u \frac{du}{\pi}$

$=\frac{-cos u}{\pi}+c$ [ c is an arbitrary constant]

Now putting the value of u

$=-\frac {cos \pi x}{\pi}+c$

(b)

$\int e^\frac{x}{2} dx$

Let $u=\frac{x}{2}$

differentiating with respect to x

$du= \frac{1}{2} dx$

2du = dx

Putting the value of x and dx

= $\int e^u.2.du$

= 2e^u +c

Now putting the value of u

$=2e^\frac{x}{2}+c$ [ c is an arbitrary constant]

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Ответ:

evarod

27.08.2022

Mathematics

As all the Angles in the Given Triangle are Equal

⇒ The Given Triangle is an Equilateral Triangle

We know that in an Equilateral Triangle all sides are Equal

Let us Equate any two sides, to find the value of x

⇒ 4x - 30 = 2x + 20

⇒ 4x - 2x = 30 + 20

⇒ 2x = 50

⇒ x = 25

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Compute the integral (a) int sin (pi x) dx by letting u = pi x. (b) int e^(x/2) dx by letting u = x/2. Show that you got the correct answer by differentiating the computed function.

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