Hasil integral 0 sampai π/3 4 sin (2x-π/2) dx adalah hal 24.... Question from @Oryn11

Verified answer

Penyelesaian:

$\int\limits^ \frac{ \pi }{3} _0 {4.sin(2x - \frac{ \pi }{2}) } \, dx$

d( $2x - \frac{ \pi }{2}$ ) = 2 dx
d( $2x - \frac{ \pi }{2}$ ) / 2 = dx

$\int\limits^ \frac{ \pi }{3} _0 {4.sin(2x - \frac{ \pi }{2}) } \, d(2x - \frac{ \pi }{2}) . \frac{1}{2}$
= $2 \int\limits^ \frac{ \pi }{3} _0 {sin(2x - \frac{ \pi }{2}) } \, d(2x - \frac{ \pi }{2})$

∫ sin x dx = -cos x

$2 \int\limits^ \frac{ \pi }{3} _0 {sin(2x - \frac{ \pi }{2}) } \, d(2x - \frac{ \pi }{2})$
= $-2.cos(2x - \frac{ \pi }{2}) ] 0-\ \textgreater \ \frac{ \pi }{3}$
= $(-2.cos(2( \frac{ \pi }{3}) - \frac{ \pi }{2}) - (-2.cos(2(0) - \frac{ \pi }{2})$
= $-2.cos( \frac{ \pi }{6}) - 2.cos( \frac{ \pi }{2})$
= -2.cos30° - 2.cos90°
= $-2. \frac{1}{2} \sqrt{3} - 0$
= $-\sqrt{3}$

4 votes Thanks 3

Komentar

Verified answer

Integral Tentu Fungsi Trigonometri.

$\displaystyle \int_{0}^{\pi /3}4\sin \left ( 2x-\frac{\pi }{2} \right )dx=-4\int_{0}^{\pi /3}\cos 2x~dx\\
=-4\left [ \frac{1}{2}\sin 2x \right ]_{0}^{\pi /3}$
$\displaystyle
=\left [ -2\sin 2\left ( \frac{\pi}{3} \right ) \right ]-\left [ -2\sin 2\left ( 0\right ) \right ]\\
=-\sqrt{3}-0\\=-\sqrt{3}$

1 votes Thanks 0

Verified answer

Verified answer

Hasil dari integral sin^2 2x cos 2x dx = hal 22

Hasil integral sec x cotan^2 x dx = hal 21

Hasil pengintegralan integral x(2+3x) dx adalah hal 21

Hasil integral 4x(x-2)^3 dx = hal 14

Hasil dari integral cos 2x akar sin 2x dx= hal 13

Hasil dari integral Sin^3 x cos x dx= lks 13

Hasil dari integral (x^2 + 2)(x^3 + 6x+1)^1/2 dx= lks 5 hal 13

Hasil pengintegralan integral (8-x)^5 dx adalah lks hal 13

Integral (sin 3x + 4 cos 2x) dx

Hasil integral sin^3 x cos x dx

Recommend Questions

Life Enjoy

Get in touch

Social