Question

3. A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move the object from x=3 to x=7?

Answer 1

$$W=\displaystyle\int_{3}^{7}(x^2-\cos(3x) +2)dx$$

$$=[\dfrac{x^3}{3}-\dfrac{1}{3}\sin (3x)+2x]\begin{matrix} 7 \\ 3 \end{matrix}$$

$$=\dfrac{343}{3}-\dfrac{1}{3}\sin (21)+14$$

$$-(\dfrac{27}{3}-\dfrac{1}{3}\sin (9)+6)$$

$$=\dfrac{340}{3}-\dfrac{1}{3}\sin (21)+\dfrac{1}{3}\sin (9)$$