Integrate using substitution tanx sec^2x dx

Step-by-step explanation:

Since I know , then I will let which will give me .

I replaced tan(x) with u and sec^2(x) dx with du.

Use the integration power rule:

Now put this back in terms of x with u=tan(x):

Check:

To check we will find the derivative of our antiderivative and see it it gives us the integrand.

By sum rule for derivatives:

Constant multiple rule will be applied to the first term while the constant rule will be applied to the second term:

Power rule+Chain rule:

Simplify the 1/2 times 2 part:

This is what our integrand was so we have confirmed are integration was correct.

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!