Question
show that intergral using identity sin2x=2sinxcosx....please #5
Show al rk in your Blve Book The full sorer If only bpnts be on a separate page in the Blue Book, completedbems a with no sopporting work, you will be awarded hal s available points The maxcimm me allowed for his exan is s0 ed half of the p exorn ss so0 mimuten, starting at the beginsitng of th cluss No extension of the tost will be psovided for 1 Find the equation of the line tangent to the e Eest will be provided for liste arrivisla graph of the function uc r l(x-3)-at the point (4, -4) Write th e equation of the line in slope-intercept torm e region bounded by the carves23, and pa-3. ive of y = (sinzat-, using logarithmic differentiation. 2 Find the aress of the region bounded by the curvess 3. Find the first derivative of y = (sinz) at Evaluate the integral f 4. dr using 2dz using trigonometric substitution 5. Show that sinx cosa: dr cos 2x -C using the identity sin 2-2 sinz cosz 6. Evaluate the integral / 3x2 sinha fully (i.e. o swer) Completee (o Find the volume of the solid generated by revolving about the v-axis the win to
Explanation / Answer
(5) We know that 2 sin x cos x = sin 2x
So, sin x cos x = (1/2) sin 2x
sin x cos x dx = (1/2) sin 2x dx = (1/2) sin 2x dx = (1/2)[-cos(2x)]/2 + C = (-1/4) cos 2x + C
