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

Show answers

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

the last choice

step-by-step explanation:

What is the equation of the circle with center (2,-5) that passes through the point (-2.10)?

Answer from: Quest

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body covers no displacement as time elapses. thus the flat line with zero gradient.

Use the drop-down menus to answer each question. which line represents the movement of a cart with a

Another question on Mathematics

Mathematics, 21.06.2019 20:30

Find the zeros of each function. f(x) = x^2 + 5x - 6

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

In dire need~! describe how to use area models to find the quotient 2/3 divided by 1/5. check your work by also finding the quotient 2/3 divided by 1/5 using numerical operations only.

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Divide. –4.2 ÷ 6 = a –0.7 b 0.7 c –7 d 7 me

Answers: 2

Answer

Mathematics, 22.06.2019 04:00

Ireally don't understand this, i'm really an idiot but i want to know how to figure this out. !

Answers: 3

Answer

You know the right answer?

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