Mathematics, 05.12.2020 08:20 samehajamal1234567

Please help! I will award brainliest and give 100 points!! Topic: calculus definite integrals and u substitution

Please help! I will award brainliest and give 100 points!!

Topic: calculus definite integrals and

Answers: 3

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Answers

Answer from: cdyshaylia55

$\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = ln3$

General Formulas and Concepts:

Pre-Calculus

Unit Circle

Calculus

Derivatives

Derivative Notation

Trig Derivatives

Integrals

Definite Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration

Logarithmic Integration

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 1 + cos(x)$ [u] Differentiate [Trig Derivative]: $\displaystyle du = -sinx \ dx$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = -\int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{-sinx}{1 + cosx}} \, dx$ [Integral] U-Substitution: $\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = -\int\limits^{\frac{1}{2}}_{\frac{3}{2}} {\frac{1}{u}} \, du$ [Integral] Logarithmic Integration: $\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = -ln|u| \bigg| \limits^{\frac{1}{2}}_{\frac{3}{2}}$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = -(-ln3)$ Simplify: $\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = ln3$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y

Answer from: Quest

i believe the answer is c.

Me, it’s the last question and i want to test out of this unit

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Please help! I will award brainliest and give 100 points!! Topic: calculus definite integrals and u...