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

The first one is 2/3the second is 1/160the third is 4/125

Answer from: Quest

the answer is y = 11.54

hope this : )

Question 8 (fill in-the-blank worth 6 points) (07.02 mc) find the measure of angle y. round your ans

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 21:00, nanda22

Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles. answer to the nearest integer.

Answers: 1

continue

Mathematics, 21.06.2019 21:30, kira3039

Aculture started with 4,000 bacteria. after 5 hours, it grew to 5,200 bacteria. predict how many bacteria will be present after 19 hours. round your answer to the nearest whole number.

Answers: 1

continue

Mathematics, 21.06.2019 22:30, vsuescun10

For the chance to be team captain, the numbers 1-30 are put in a hat and you get two chances to pick a number, without replacement. which formula correctly shows how to find the probability that you choose the number 1 and then 2?

Answers: 1

continue

Mathematics, 22.06.2019 03:00, cerna

He letter p on the number line below represents the number . (use the hyphen for negative numbers and write answer as a decimal, such as –7.2) number line from negative 7 to positive 7 in increments of 0.5 is shown. only the whole numbers are labeled. a point labeled p is placed at the eleventh tick mark to the left of 0.

Answers: 3

continue

You know the right answer?

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