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Integrate the function $\sec\left(x\right)\left(2\tan\left(x\right)-5\sec\left(x\right)\right)$ from 0 to $\frac{\pi}{4}$

Step-by-step Solution

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Final Answer

$-4.171572$
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Step-by-step Solution

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Rewrite the integrand $\sec\left(x\right)\left(2\tan\left(x\right)-5\sec\left(x\right)\right)$ in expanded form

$\int_{0}^{\frac{\pi}{4}}\left(2\tan\left(x\right)\sec\left(x\right)-5\sec\left(x\right)^2\right)dx$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{\frac{\pi}{4}}\left(2\tan\left(x\right)\sec\left(x\right)-5\sec\left(x\right)^2\right)dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function sec(x)(2tan(x)-5sec(x)) from 0 to pi/4. Rewrite the integrand \sec\left(x\right)\left(2\tan\left(x\right)-5\sec\left(x\right)\right) in expanded form. Expand the integral \int_{0}^{\frac{\pi}{4}}\left(2\tan\left(x\right)\sec\left(x\right)-5\sec\left(x\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{\frac{\pi}{4}}2\tan\left(x\right)\sec\left(x\right)dx results in: 0.828428. The integral \int_{0}^{\frac{\pi}{4}}-5\sec\left(x\right)^2dx results in: -5.

Final Answer

$-4.171572$

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Function Plot

Plotting: $\sec\left(x\right)\left(2\tan\left(x\right)-5\sec\left(x\right)\right)$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

3. See formulas

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