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
Good for Caleb, he better have bought cheese.
What do you mean by this The area of the paralleogram is 184 units squaredgive me your full question then i can help you
Side length = 16.7 cm
Solution:
Perimeter of a square given = 66.8 cm
In a square four sides are equal.
The perimeter of a square = 4 × side
⇒ 4 × side = 66.8 cm
Divide both sides of the equation by 4 to equal the expression.
⇒ side = 66.8 ÷ 4
⇒ side = 
⇒ side = 16.7 cm
Hence, the side length of the square is 16.7 cm.
