Evaluate the integral.
∫(sec²(t) i+t(t²+1)⁵j+t⁴ln(t)k)dt
Evaluate the integral.∫(sec ²(t) i+t(t²+1)⁵ j+t⁴ ln (t) k) d t
12. Evaluate the integral.∫(sec ²(t) i+t(t²+1)⁵ j+t⁵ ln (t) k) d t13. Find r(t) if r'(t)=t⁵ i+e^{t} j+3te³t k and r(0)=i+j+k.14.Find f'(2), where f(t)=u(t) · v(t), u(2)=(1,2,-1), u'(2)=(3,1,7), and v(t)=(t, t2), t3).
Evaluate the definite integral. ∫6 to 1 t^4 ln(4t)dt
Evaluate the indefinite integral\ sec^2 t sqrt 1 + tant t dt Use the previous answer to evaluate between t=0 and t = pi / 4 1. Evaluate the indefinite integral ſ secº (t)/1+tan(t) dt (7 pts) 2. Use the previous answer to evaluate betweent O and t = 4 TT (3 pts)
7. (10 points) Evaluate integral ſeti + sint j + 1 k) dt. 2t-1
Part A Evaluate the integral: I= j (+5 + 5) (8 (t) + 128 (t – 1)) dt. Express your answer using three significant figures. View Available Hint(s) VO AXO Ut vec 2 ? Submit Part B Evaluate the integral: I = ſ t® [8 (t) + 8(t + 1.8) + 8(t – 3)] dt. Express your answer using three significant figures. View Available Hint(s) ran Use step functions to write the expression for the function shown in (Figure 1)....
Evaluate the integral (-8 sin(t)- 4 cos() dt ntegral Evaluate the integral (-8 sin(t)- 4 cos() dt ntegral
Evaluate the folloMing integrals. Sec (x) d fe I+E dt Evaluate the folloMing integrals. Sec (x) d fe I+E dt
Evaluate the line integral in Stokes Theorem to evaluate the surface integral J J(VxF)-n ds. Assume that n points in an upward direction F (xty,y z,z+x) S is the tilted disk enclosed by r()-(3 cost,4sint,7 cos t Rewrite the surface integral as a line integral. Use increasing limits of integration. dt (Type exact answers, using π as needed.) Find the value of the surface integral. JÍs×F).nds-ロ (Type an exact answer, using π as needed.) Evaluate the line integral in Stokes...
5. Evaluate the integral sec" x dr. 6. Evaluate the integral I 2 dx X3 V x2 – 1 >1. 7. Evaluate the integral dc I VAI 8. Evaluate the integral 19 - 22 dc. .x2