Vector Integration Homework: Evaluate Integrals A⋅B & A×B

[yusukered07]

Homework Statement

If A(t) = t i - t² j + (t - 1) k and B(t) = 2t² i + 6t k, evaluate (a) \int^{2}_{0}A \cdot B dt, (b) \int^{2}_{0}A \times B dt.

Homework Equations

The Attempt at a Solution

Help me please because I don't know how to solve this problem. Thanks!

Looking forward to your responses.

 

[Dustinsfl]

Take the dot product for the first and then integrate and take the cross product for the second. Dot product remember is Ai*Bi + Aj*Bj + Ak*Bk. For cross product, set up a matrix with i j k in row one followed by the i j k of a in row 2 and i j k of b in row 3

 

[yusukered07]

Take the dot product for the first and then integrate and take the cross product for the second. Dot product remember is Ai*Bi + Aj*Bj + Ak*Bk. For cross product, set up a matrix with i j k in row one followed by the i j k of a in row 2 and i j k of b in row 3

Thanks! I've got the answer..