Mathematics, 15.07.2019 04:00 celestemaria0727

Evaluate the definite integral. use the integration capabilities of a graphing utility to verify your result. π/24 cos(12x) 0 dx

Answers: 1

Show answers

Answers

Answer from: mayaa2351

$\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx = \frac{1}{12}$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals

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

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

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 12x$ [u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = 12 \ dx$ [Bounds] Switch: $\displaystyle \left \{ {{x = \frac{\pi}{24} ,\ u = 12(\frac{\pi}{24}) = \frac{\pi}{2}} \atop {x = 0 ,\ u = 12(0) = 0}} \right$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx = \frac{1}{12}\int\limits^{\frac{\pi}{24}}_0 {12\cos (12x)} \, dx$ [Integral] U-Substitution: $\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx = \frac{1}{12}\int\limits^{\frac{\pi}{2}}_0 {\cos (u)} \, du$ [Integral] Trigonometric Integration: $\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx = \frac{1}{12}[-sin(u)] \bigg| \limits^{\frac{\pi}{2}}_0$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx = \frac{1}{12}(1)$ Simplify: $\displaystyle \int\limits^{\frac{\pi}{24}}_0 {\cos (12x)} \, dx = \frac{1}{12}$

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

Unit: Integration

Answer from: Quest

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

Answer from: Quest

false

step-by-step explanation:

the reason i say this is because for a certain length of sides you can pick any two and the length is wither equal or greater than the third side and in this case it's not.

3 + 5 = 8

8 is smaller than 9 which is the third side.

hope this : )

Another question on Mathematics

Mathematics, 22.06.2019 00:30

Bocephus has a bag full of nickels and dimes. if there are 3 times as many dimes as nickels, and he has $\$36.05$ in his bag, how many nickels does he have?

Answers: 1

Answer

Mathematics, 22.06.2019 02:40

Kilgore trout creates a new scale to diagnose depression. however, his scale only assesses one symptom of depression while ignoring others. which of the following is his new scale most likely lacking? a) test-retest reliability b) discriminant validity c) criterion validity d) alternate-forms reliability e) content validity f) none of the above

Answers: 1

Answer

Mathematics, 22.06.2019 03:00

Which angle of rotation is an angle of rotational symmetry for all figures?

Answers: 2

Answer

Mathematics, 22.06.2019 04:00

Which ordered pair makes both inequalities true? y< 3x-1 and y> -x+4 4,0 1,2 0,4 2,1

Answers: 3

Answer

You know the right answer?

Evaluate the definite integral. use the integration capabilities of a graphing utility to verify you...