Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0
Answer:
<h2>M = ( 5 , 2)</h2>
Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
A(12,9), B(-2,-5)
The midpoint M is
We have the final answer as
<h3>M = ( 5 , 2)</h3>
Hope this helps you
Answer:
The measurement of AB is 16.25 units.
Step-by-step explanation:
In right triangle ABC, ∠C is a right angle, m∠A = 52° , AC = 10.01, and AB = c.
We need to find the measurement of AB.
∠C is a right angle, it means AB is hypotenuse.
In a right angle triangle,
Hence, the measurement of AB is 16.25 units.
Answer:
The prime factors are: 2 x 2 x 59
or Written in exponential form: 2^2 x 59^1
Step-by-step explanation:
236 ÷ 2 = 118 - No remainder! 2 is one of the factors
118 ÷ 2 = 59 - No remainder! 2 is one of the factors
59 ÷ 59 = 1 - No remainder! 59 is one of the factors
together we have the factors 2 x 2 x 59 = 236
Answer:
x=-8 and y=9
Step-by-step explanation:
rewrite the equations to x+2y=10,3x+4y=12
sub 2y from both sides x+2y-2y=10-2y
substitue x=10-2y in 3x +4y=12
3(-2y+10)+4y=12
distribute
add-30 to both sides
divide both sides by -2
y=9
sustitute 9 for y in -2y+10=x
x=-8
