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# Compute a vector valued integral

Compute the vector valued integral We compute # Compute the vector valued integral

Compute the vector valued integral We compute, # Compute the integral of (sin t, cos t, tan t)

Compute the vector-valued integral We compute # Compute the integral of (t, t1/2, et)

Compute the vector-valued integral We compute, # Prove that the angle between F(t) and F'(t) is constant for a given vector function

Consider the vector-valued function Prove that the angle between and is a constant.

Proof. First, we have Thus, Hence, and are orthogonal, so the angle between them is constant, # Compute derivatives of F(t) = log (1+t2) i + arctan t j + 1/(1+t2) k

Compute the derivatives and of the vector valued function We compute # Compute derivatives of F(t) = cosh t i + sinh (2t) j + e-3tk

Compute the derivatives and of the vector valued function We compute # Compute derivatives of F(t) = 2eti + 3etj

Compute the derivatives and of the vector valued function We compute, # Compute derivatives of F(t) = (arcsin t, arccos t)

Compute the derivatives and where is the vector valued function We compute # Compute derivatives of F(t) = (cos t, sin2 t, sin (2t), tan t)

Compute the derivatives and of the vector valued function We compute 