All categories

3 years ago

Evalute the integral (sin^3 (x)/cosx)dx

1 answer:

8 0

$\int { \frac{sin ^{3} x}{cos x} } \, dx= \\ = \int { \frac{sin ^{2} x*sin x}{cos x} x} \, dx= \\ = \int { \frac{(1-sin ^{2} x)*sinx}{cos x} } \, dx =$
t = cos x,
dt = - sin x dx;
$= \int { \frac{-(1- t^{2}) }{t} } \, dt= \\ = \int { \frac{t ^{2}-1 }{t} } \, dt = \\ =\int {t} \, dt - \int { \frac{1}{t} } \, dt = t^{2}- ln t = \\ = \frac{cos ^{2} x}{2}-ln ( cos x ) + C$

You might be interested in

Four brothers have ages which are consecutive even integers. If the product of the ages of the two middle brothers is 528, how o

exis [7]

Answer:

The oldest brother is of age $26$ years.

Step-by-step explanation:

As the age of four brothers are consecutive even integers.

We assume that the ages are $x,(x+2),(x+4),(x+6)$ as their respective ages.

And the age of the youngest brother $x$ yrs.

Age of the oldest brother $(x+6)$ yrs.

According to the question

Product of two middle brother that is $(x+2)(x+4) =528$

So we will arrange this in our equation and solve the quadratic.

$(x+2)(x+4) =528$

$x^{2}+4(x)+2(x)+8 =528$

$x^{2}+4(x)+2(x)+8-528=0$

$x^{2}+6(x)-520=0$

Solving the quadratic by using middle term splitting or directly with quadratic formula we can find the value of 'x' .

Here it is solved with quadratic formula:

Comparing with standard equation $ax^{2}+b(x)+c=0$ ,here $a=1,b=6\ and\ c=-520$ .

$x= \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \frac{-6 \pm \sqrt{6^2-4\times \ (-520)} }{2\times 1}$

$x=20,-26$

We will work with the positive value of (x) so the the age of the youngest brother $=(x)=20$ yrs.

And the age of the the oldest brother $=(x+6)=(20+6)=26$ years.

The age difference is of $(26-20)=6$ years.

4 0

4 years ago

Simplify the following expression. (0.5x – 3)(0.5x + 3)

Aloiza [94]

Answer:

0.25x^2-9

Step-by-step explanation:

Difference of squares converse:

0.25x^2-9

4 0

3 years ago

Read 2 more answers

Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5),

ivanzaharov [21]

An expression, that is a function, will have no x-repeats on the x,y pairs.

and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then,

$\bf a \qquad\{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)\}\\\\
b \qquad\{(-1, 2), (0, \stackrel{\downarrow }{4}), (1, 5), (5, \stackrel{\downarrow }{4}), (7, 2)\}\impliedby 
\begin{array}{llll}
\textit{notice the } y-rep eats\\
\textit{thus, no dice}
\end{array}$

$\bf c \qquad\{(-1, -2), (0, \stackrel{\downarrow }{4}), (1, 3), (5, 14), (7, \stackrel{\downarrow }{4})\}\impliedby 
\begin{array}{llll}
\textit{notice the } y-rep eats\\
\textit{thus, no dice}
\end{array}\\\\
d \qquad\{(-1, \stackrel{\downarrow }{4}), (0, \stackrel{\downarrow }{4}), (1, 2), (5, 3), (7, 1)\}\impliedby 
\begin{array}{llll}
\textit{notice the } y-rep eats\\
\textit{thus, no dice}
\end{array}$

6 0

3 years ago

Read 2 more answers

Given that the length of the side of a right square-based prism is 5 inches, and its volume is 125 cubic inches, find its height

hram777 [196]

Answer:

A. 5 in.

Step-by-step explanation:

A square prism is another name for cube, and all vertices, edges, and faces are congruent, so this is an automatic giveaway.

I am joyous to assist you anytime.

5 0

4 years ago

At a school number of boys:number of girls = 1:9 there are 124 more boys than girls. Work out the total number of students at th

kykrilka [37]

124 x 9 = the amount of girls which is 1116 then add the boys which is 124 so 1116 + 124 = 1250. After i did that i relized your question dont make sense

3 0

3 years ago