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lesya692 [45]
3 years ago
12

Show how to make a ten to fund 12-4 write the number sentence

Mathematics
2 answers:
Strike441 [17]3 years ago
6 0
10-4 =6 that is the answer
dexar [7]3 years ago
3 0
Subtract 2 from 12. 12-2 is 10. You can subtract 10 with 4, and then add 2. (10-4)+2=8.
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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}}
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