Posted by **Tracy** on Saturday, November 19, 2011 at 10:10pm.

Evaluate the integral of

(x)cos(3x)dx

A. (1/6)(x^2)(sin)(3x)+C

B. (1/3)(x)(sin)(3x)-(1/3)(sin)(3x)+C

C. (1/3)(x)(sin)(3x)+(1/9)(cos)(3x)+C

D. (1/2)(x^2)+(1/18)(sin)^2(3x)+C

- calculus -
**drwls**, Saturday, November 19, 2011 at 10:50pm
An easy way to do this is to take the derivatives of the four choices, and see what gives you back the original function.

The derivative of function C. is

(1/3)sin(3x) + (x/3)*3*cos(3x) -(3/9)sin(3x) = x cos(3x)

Looks like a winner to me.

- calculus -
**Steve**, Sunday, November 20, 2011 at 7:05am
Just as easy as taking all those derivatives (to me anyway) is to use integration by parts:

u = x

du = dx

dv = cos 3x dx

v = 1/3 sin 3x

Int(u dv) = uv - Int(v du)

= x/3 sin 3x - Int(1/3 sin 3x dx)

= x/3 sin 3x + 1/9 cos 3x

= (C)

PS (sin)(3x) is bogus notation. (sin) is not a value like (1/3) or (x). It is a function.

Try (sin(3x))

## Answer This Question

## Related Questions

- tigonometry - expres the following as sums and differences of sines or cosines ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- algebra - Can someone please help me do this problem? That would be great! ...
- Integral - That's the same as the integral of sin^2 x dx. Use integration by ...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- Calculus - Evaluate the integral. S= integral sign I= absolute value S ((cos x...
- Trigonometry - Solve the equation for solutions in the interval 0<=theta<...
- Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
- Trig - Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are ...

More Related Questions