Exercises on the calculation of primitives are crucial for high school seniors in the United States education system. These exercises cover various concepts and calculation techniques that are at the core of the mathematics curriculum, allowing students to practice independently with hints, course reminders, and methodological advice.
For example, one exercise asks students to calculate a primitive of a rational function of the first degree over the set of positive real numbers. This exercise aims to use the natural logarithm to determine one of the primitives of a rational fraction, thereby reinforcing students' understanding of logarithmic properties and their application in the calculation of primitives.
Another exercise focuses on calculating a primitive of a rational function of the second degree over the set of positive real numbers. Here, the objective is to use the natural logarithm to compute the primitive of a rational fraction, helping students master more advanced techniques in integral calculus.
Finally, an additional exercise proposes finding a primitive of a polynomial function. Students must use integration methods to calculate one of the primitives of this function, ensuring that the primitive function is zero at a certain point. This exercise allows students to apply the principles of integration to solve concrete problems involving the calculation of primitives of polynomial functions.
These exercises are designed to reinforce students' understanding and prepare them for exams by providing thorough and varied practice in the methods of calculating primitives.
3 exercisesExercise example N°1713 :
Compute an antiderivative of the function `f(x)=7/(9+7*x)` on `RR^+` .
neperian logarithm antiderivatives functions 12th Grade antiderivative
The aim of this corrected exercise is to use the neperian logarithm to calculate one of the primitives of a rational fraction of the first degree.
Exercise example N°1714 :
Compute an antiderivative of the function `f(x)=(8*x)/(1+4*x^2)` on `RR^+` .
neperian logarithm antiderivatives functions 12th Grade antiderivative
The goal of this corrected exercise is to use the neperian logarithm for antiderivative calculation of a rational fraction of degree 2.
Exercise example N°1740 :
Let f be the function defined by f(x)= `3-2*x^2+x^3` ,compute an antiderivative of f, `F(x)`, with F(x)=0.
antiderivatives functions 12th Grade integral
The aim of this corrected exercise is to use integration methods to calculate one of the antiderivative of a polynomial function.