You visited us 1 times! Enjoying our articles? Unlock Full Access!

General Solution of Trigonometric Equation

If for a real...

Question

If for a real number $y, [y]$ is the greatest integer less than or equal to $y$ , then value of the integral $\int_{\frac{π}{2}}^{\frac{3 π}{2}} [2 sin x] d x$ is $\frac{π}{a}$ where value of $a$ is

Open in App

Solution

$I = \int_{\frac{π}{2}}^{\frac{5 π}{6}} (1) d x + \int_{\frac{5 π}{6}}^{π} (0) d x + \int_{π}^{\frac{7 π}{6}} (- 1) d x + \int_{\frac{7 π}{6}}^{\frac{3 π}{2}} (- 2) d x$
$I = (\frac{5 π}{6} - \frac{π}{2}) + 0 - (\frac{7 π}{6} - π) - 2 (\frac{3 π}{2} - \frac{7 π}{6})$
$I = - \frac{π}{2} \Rightarrow a = - 2$

Suggest Corrections

Similar questions

y, [y]

y

\frac{3 π}{2} \int \frac{π}{2} [2 sin x] d x

[y]

y

\int_{π / 2}^{3 π / 2} [2 sin x]

y

[y] =

x

\int_{\frac{π}{2}}^{\frac{3 x}{2}} [2 sin x] d x

y, [y]

y

\frac{3 π}{2} \int \frac{π}{2} [2 sin x] d x

\int_{π / 2}^{3 π / 2} [2 sin x] d x

[x]

Join BYJU'S Learning Program