1. Find the general antiderivative. 4* cosx/sin^2x (dx) 2. Find the general anti
ID: 2863635 • Letter: 1
Question
1. Find the general antiderivative.
4* cosx/sin^2x (dx)
2. Find the general antiderivative.
(4x-2e^x)dx
3. Find the general antiderivative.
3/4x^2+4 dx
4. Find the function f(x)satisfying the given conditions.
f " (x)= 20x^3+2e^2x, f ' (0)= -3, f(0)=2
5. Determine the position function if the velocity function is v(t)=3e^-1-2 and the initial position is s(0)=0.
6. Write out all terms and compute the sums.
7
E (i^2+i)
i=3
7. Use summation rules to compute the sum.
140
E (n^2+2n-4)
n=1
8. Use summation rules to compute the sum.
20
E (i-3) (i+3)
i=4
9. Compute sum of the form n (summation)i=1for the given values of .
f(x) =3x+5, x=0.4, 0.8, 1.2,1.6, 2.0, deltax=0.4; n=5
10. Compute sum of the form for the given values of .
11. Approximate the area under the curve on the given interval using n rectangles and the evaluation rules (a) left endpoint, (b) midpoint, and (c) right endpoint.
y= x^2+1 on [0, 2], n = 16
12. Approximate the area under the curve on the given interval using n rectangles and the evaluation rules (a) left endpoint, (b) midpoint, and (c) right endpoint.
y=e^-2x on [–1, 1], n = 16
13. Use Riemann sums (See Section 4.3) and a limit to compute the exact area under the curve.
y=x^2+3x on (a) [0, 1]; (b) [0, 2]; (c) [1, 3]
14. Use Riemann sums (See Section 4.3) and a limit to compute the exact area under the curve.
y=4x^2-x on (a) [0, 1]; (b) [–1, 1]; (c) [1, 3]
15. Construct a table of Riemann sums as in example 3.4 (See Section 4.3) of the text to show that sums with right-endpoint, midpoint, and left-endpoint evaluation all converge to the same value as .
F(x) =sin x [ 0, pi/2]
16. Evaluate the integral by computing the limit of Riemann sums.
2
-2 (x^2-1)dx
17. Write the given (total) area as an integral or sum of integrals.
The area above the x-axis and below y=4x-x^2
18. Use the given velocity function and initial position to estimate the final position s(b).
v(t)= 30e^-1/4, s(0)=-1, b=4
19. Compute the average value of the function on the given interval.
f(x)= x^2+2x, [0,1]
20. Use the Integral Mean Value Theorem (See Section 4.4) to estimate the value of the integral.
1 3/x^3+2 (dx)
-1
Explanation / Answer
1. Find the general antiderivative.
4* cosx/sin^2x (dx)
4(sinx)-2 cosx (dx)
=4(1/(-2+1))(sinx)-2+1+C
=-4(sinx)-1+C
=(-4/(sinx)) +C
2. Find the general antiderivative.
(4x-2e^x)dx
=4*(1/2)x2 -2ex +C
=2x2 -2ex +C
3. Find the general antiderivative.
(3/4)x^2+4 dx
=(3/4)(1/3)x3 +4x +C
=(1/4)x3 +4x +C
4. Find the function f(x)satisfying the given conditions.
f " (x)= 20x3+2e2x ,f ' (0)= -3, f(0)=2
f '(x)= 20x3+2e2x dx
f '(x)=20(1/4)x4+2(1/2)e2x+C
f '(x)=5x4+e2x+C
f '(0)=-3
5*04+e0+C=-3
0+1+C=-3
C=-4
f '(x)=5x4+e2x-4
f(x)= 5x4+e2x-4 dx
f(x)=5(1/5)x5+(1/2)e2x-4x +C
f(x)=x5+(1/2)e2x-4x +C
f(0)=2
0+(1/2)e0-0+C=0
(1/2)+C=0
C=-1/2
f(x)=x5+(1/2)e2x-4x -(1/2)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.