Evaluate the integral.
∫(sec ²(t) i+t(t²+1)⁵ j+t⁴ ln (t) k) d t
Evaluate the integral.∫(sec²(t) i+t(t²+1)⁵j+t⁴ln(t)k)dt
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
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
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)
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)....
Let u(t) =t^3 i + ln(t) j + e^2t k and v(t) = 1/t^3 i + 2 j + t k 2. Let u(t) - ti+In(t)j+ et k and Compute the derivative of the dot product f u(t)v() in two ways and confirm they agree: Compute the dot product u(t) v(t) first and then differentiate the result. . Alternatively, use the following "Dot Product Rule" u(t) v(t)] u'(t) v(t)+ u(t) v'(t) Aside: It's worth noting that there are other forms...
7. (10 points) Evaluate integral ſeti + sint j + 1 k) dt. 2t-1
Evaluate the integral from 1 to infinity of ln(x)/(x)7.
Evaluate the Integral [sec" sec+ xVtan x dx