The value of b a -x7-sin xcos xdx where a-b-0 is

The correct option is A 2b asin(b a) Solution:Given that: a+b=0 i.e. a= b ∫_a^bx^7+sin xcos xdx =∫_ b^bx^7+sin xcos xdx =∫_ b^b(x ...

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Byju's Answer

Standard XII

Mathematics

Integration of Piecewise Continuous Functions

The value of ...

Question

The value of $b \int a \frac{x^{7} + sin x}{cos x} d x$ where $a + b = 0$ is

2 b - a sin (b - a)

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a + 3 b cos (b - a)

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sin a - (b - a) cos b

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0

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Solution

The correct option is A $2 b - a sin (b - a)$
Solution:
Given that:
$a + b = 0$ i.e. $a = - b$
$\int_{a}^{b} \frac{x^{7} + sin x}{cos x} d x$
$= \int_{- b}^{b} \frac{x^{7} + sin x}{cos x} d x$
$= \int_{- b}^{b} (\frac{x^{7}}{cos x} + \frac{sin x}{cos x}) d x$
$= \int_{- b}^{b} (x^{7} sec x + tan x) d x$
The given integrand is an odd function.
Therefore, its answer is 0.
Hence, D is the correct option.

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Similar questions

Q. Prove that:
(i)

\frac{\cos (A + B + C) + \cos (- A + B + C) + \cos (A - B + C) + \cos (A + B - C)}{\sin (A + B + C) + \sin (- A + B + C) + \sin (A - B + C) - \sin (A + B - C)} = \cot C

(ii) sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0

Prove that:
(i) $\frac{c o s (A + B + C) + c o s (- A + B + C) + c o s (A - B + C) + c o s (A + B - C)}{s i n c o s (A + B + C) + s i n c o s (- A + B + C) + s i n c o s (A - B + C) - s i n (c o s (A + B - C))}$
(ii) $s i n (B - C) c o s (A - D) + s i n (C - A) c o s (B - D) + s i n (A - B) c o s (C - D) = 0$

Q. Show that:
(i) sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0
(ii) sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0

Q. If

sin A + sin B + sin C = 0

and

cos A + cos B + cos C = 0

, then the value of

sin (\frac{A - B}{2})

(where A, B, C \in [0, 2 π])

Find b

lim x \to 0 [\frac{sin (x + a) + sin (a - x) - 2 sin a}{x sin x}]

= - b sin a .

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The value of b∫ax7+sinxcosxdx where a+b=0 is

The correct option is A 2b−asin(b−a)Solution:Given that:a+b=0 i.e. a=−b∫bax7+sinxcosxdx=∫b−bx7+sinxcosxdx=∫b−b(x7cosx+sinxcosx)dx=∫b−b(x7secx+tanx)dxThe given integrand is an odd function.Therefore, its answer is 0.Hence, D is the correct option.

The value of $b \int a \frac{x^{7} + sin x}{cos x} d x$ where $a + b = 0$ is