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
Using it's concept, it is found that the coefficient of the mathematical expression 7m² + 2(19) is of 7.
<h3>What is the leading coefficient of a polynomial?</h3>
The leading coefficient of a polynomial is the <u>term that multiplies the highest exponent</u>.
In this problem, the expression is given by:
7m² + 19.
The highest exponent is of 2, in m², hence the leading coefficient is of 7.
More can be learned about the coefficient of a mathematical expression at brainly.com/question/24380382
#SPJ1
A = hw
Replace h with 4h
Replace w with 4w
A = (4w)(4h)
= 16hw
The area becomes 16 times larger.
Have an awesome day! :)
Every day that person consumes <span>1.87561643836 pounds of fruit and vegetables in a day.</span>
Answer:
"between 30 yards and 150 yards"
Step-by-step explanation:
Let one side of a triangle be x and another side be y. To find the possible lengths of the third side, it is given by:
<u><em>Possible length of 3rd side would be between "x - y" and "x + y"</em></u>
<u><em /></u>
Here, given x = 90 and y = 60, so the possible length of 3rd side would be:
90 - 60 = 30,
90 + 60 = 150
Hence, in between 30 and 150
