# Integral calculus: answer key to senior math exercises in PDF.

The answer to the math exercises in the final year of high school on the calculation of an integral using an intermediate integral, as well as the property of linearity (additivity).

Exercise 1:

Calculate

by looking for an intermediate integral of the form

that will easily fit in.

We consider the integral:

Let’s calculate:

so

Exercise 2:

Calculate these integrals by integrating by partials:

A. .

Let u=x u’=1

and

Exercise 3:

Let be the function defined on by .

What is the derivative of on ?

Exercise 4:

Exercise 5:

Exercise 6:

Consider the sequence defined, for any natural number n , by :

1.

a. Show that .

b. Calculate , deduce .

2. Show that, for any natural number n, .

3.

a. Show that, for any non-zero natural number n,

b. Deduce that, for any non-zero natural number n,

4. Determine the limit of the sequence .

Exercise 7:

Exercise 8:

Exercise 9:

Calculate:

and

Exercise 10:

a.

b.

c.

d.

d.

e.

f.

g.

h.

i.

j.

k.

l.

m.

Exercise 12:
We consider three real numbers a,b,c such that, for all :

.

.

.

By identification, we obtain the system :

so

2. Let .

a. Calculate

.

b. Let f be the function defined on by

By integrating by parts, calculate f(X) as a function of X .

u(x)= lnx then

then

So:

c. gold :

therefore:

Exercise 14:
Calculate the proposed integral:

a.

b.

c.

d.

e.

f.

g.

h.

Exercise 15:

Either

Exercise 16:

We consider

and

a.

b.

Exercise 17:

because the function is odd on the interval [-5;5] centered in 0.

## Answers to the exercises on integrals in high school.

After having consulted the answers to these exercises on integral calculus in the final year of high school, you can return to the exercises in the final year of high school.

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