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Integration of Trigonometric Functions

Evaluate: 35...

Question

Evaluate: $35 - [15 + 14 - (13 + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 - 1 + 3)$ ].

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Solution

To evaluate an expression , we must first simplify the expression below the vinculum, then inside the small bracket , then inside the curly bracket , and finally inside the square bracket using the DMAS rule,

Thus, $35 - [15 + 14 - (13 + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 - 1 + 3)]$

$= 35 - (15 + 14 - (13 + 4))$

[Removing vinculum]

$= 35 - (15 + 14 - 17)$
[Removing small bracket]

$= 35 - 12$
[Removing curly bracket]

$= 23$

$∴$ The value of $35 - [15 + 14 - (13 + ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 - 1 + 3)$ ] is $23$ .

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Q. Evaluate:

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\frac{- 3}{5} + \frac{7}{5} + \frac{- 1}{5}

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Evaluate each of the following: $(i) \frac{2}{3} - \frac{3}{5} (i i) \frac{- 4}{7} - \frac{2}{- 3} (i i i) \frac{4}{7} - \frac{- 5}{- 7} (i v) - 2 - \frac{5}{9} (v) \frac{- 3}{- 8} - \frac{- 2}{7} (v i) \frac{- 4}{13} - \frac{- 5}{26} (v i i) \frac{- 5}{14} - \frac{- 2}{7} (v i i i) \frac{13}{15} - \frac{12}{25} (i x) \frac{- 6}{13} - \frac{- 7}{13} (x) \frac{7}{24} - \frac{19}{36} (x i) \frac{5}{63} - \frac{- 8}{21}$

Evaluate the following :

(i) $^{14} C_{3}$ (ii) $^{12} C_{10}$

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