Given that the antiderivative of f of x equals 1 divided by the quantity x squared plus 1 is f(x) = tan-1(x) + c, evaluate the integral from negative 1 to 1 of the 1 divided by the quantity x squared plus 1, dx . (4 points) a. pi b. pi over 2 c. pi over 4 d. 0

You know that if f(x) = 1/(x²+1) then F(x)=arctan(x).

What is arctan(x) function? It is inverse function of tan(x) in tge range (-π/2, π/2).

So if tan(x) = y then x = arctan(y)

therefore arctan(-1) = -π/4 because tan(-π/4)=-1 and arctan(1)=π/4 because tan(π/4) = 1.

In conclusion:

integral (dx/(x²+1)) from -1 to 1 =

= F(1) - F(-1) = arctan(1) - arctan(-1) =

=π/4-(-π/4)=π/4+π/4 = π/2.

answer B is correct

B. π/2.

Step-by-step explanation:

We need the value of:

1

∫ 1 / (x^2 - 1) dx  =     [ tan-1(1) - tan-1(-1) ]  = π/4 - (-π/4) = π/2.

-1

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.