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vredina [299]
3 years ago
8

Which pairs of faces will be opposite one another when the prism is created? Check all that apply.

Mathematics
2 answers:
blondinia [14]3 years ago
7 0
A&C
B&F
Try it by fold the prism with paper
Amiraneli [1.4K]3 years ago
7 0

Answer:

The answers are A&B  B&C, and A&F

Step-by-step explanation:

Any of these are equal and that is the question about

hope its helpful

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Evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx
Vadim26 [7]

Answer:

\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + 1 - \frac{\sqrt{3}}{2}

General Formulas and Concepts:

<u>Calculus</u>

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:                                                           \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

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

Integration Property [Addition/Subtraction]:                                                   \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx

<u>Step 2: Integrate</u>

  1. [Integral] Rewrite [Integration Property - Addition/Subtraction]:           \displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {x} \, dx + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx
  2. [Left Integral] Integration Rule [Reverse Power Rule]:                           \displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx
  3. [Right Integral] Trigonometric Integration:                                             \displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \sin x \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}}
  4. Integration Rule [Fundamental Theorem of Calculus 1]:                         \displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + \bigg( 1 - \frac{\sqrt{3}}{2} \bigg)

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

Unit: Integration

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