Let an-0- -4tannxdx- Then a2-a4-a3-a5- a4-a6 are in

The correct option is A HP a _ 2 + a _ 4 =∫ _ 0 ^π #160;/ 4 #160; tan ^ 2 x+ tan ^ 4 x = #160; ∫ _ 0 ^π #160;/ 4 #160; tan ^ 2 x sec ^ 2 x ...

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Byju's Answer

Standard XII

Mathematics

Integration by Partial Fractions

Let an=∫0π ...

Question

Let $a_{n} = \int_{0}^{π / 4} t a n^{n} x d x$ . Then $a_{2} + a_{4}, a_{3} + a_{5}, a_{4} + a_{6}$ are in

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Solution

The correct option is A HP
$a_{2} + a_{4} = \int_{0}^{\frac{π}{4}} {t a n}^{2} x + {t a n}^{4} x$
= $\int_{0}^{\frac{π}{4}} {t a n}^{2} x {s e c}^{2} x$
= $\frac{1}{3}$
$a_{3} + a_{5} = \int_{0}^{\frac{π}{4}} {t a n}^{3} x {s e c}^{2} x$
= $\frac{1}{4}$
$a_{4} + a_{6} = \int_{0}^{\frac{π}{4}} {t a n}^{4} x {s e c}^{2} x$
= $\frac{1}{5}$
3, 4, 5 are in A.P.
$\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ are in H.P.

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Similar questions

Q. Let

a_{n} = \int_{0}^{\frac{π}{4}} {tan}^{n} x d x .

Then

a_{2} + a_{4}, a_{3} + a_{5}, a_{4} + a_{6}

are in

Q. Suppose

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

are integers such that

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

where

0 \leq a < j

for

j = 2, 4, 5, 6, 7.

The sum

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

Q. Suppose

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

are intagers such that

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

where

0 \leq a_{j} < j

for

j = 2, 3, 4, 5, 6, 7

. The sum

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

is-

Suppose $a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}$ are integers such that $\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}$ where 0 $\leq$ a< j for j= 2,4,5,6,7.

The sum $a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}$ is

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Let an=∫π/40tannxdx. Then a2+a4,a3+a5,a4+a6 are in

The correct option is A HPa2+a4=∫π40tan2x+tan4x= ∫π40tan2xsec2x= 13a3+a5=∫π40tan3xsec2x= 14a4+a6=∫π40tan4xsec2x= 153, 4, 5 are in A.P.13,14,15 are in H.P.

Let $a_{n} = \int_{0}^{π / 4} t a n^{n} x d x$ . Then $a_{2} + a_{4}, a_{3} + a_{5}, a_{4} + a_{6}$ are in