Antiderivative Class 12 Mathematics Solutions PDF is very much important for those students who wants to create a meat and tidy notes. When you create your mathematics notes by using our solutions PDF, you don’t need to take the risk of making mistakes because we already have solved all the questions. In this article you’ll get the complete solution of exercise class 12 antiderivatives third exercise. You can also download the solutions PDF if you want to view them offline.
Chapter – 14
Antiderivative
In class 12 antiderivative chapter we will study somehow different types of questions than that we have learned in class 11. The solutions we have got while solving the antiderivative questions in class 11 will be used as formulas in grade 12. So before you start solving questions of any chapter, make sure to read all the required formulas.
Class 12 Antiderivative chapter has 4 exercises in total and in each exercise we will learn the trick of solving different types of questions. We already have provided the notes of other exercises. So if you haven’t completed the notes of previous exercise then try to complete them before starting this one.
What is Antiderivative?
The antiderivative of a function refers to the inverse operation of finding the derivative of that function. In mathematical terms, we also refer to the antiderivative as the integral of a function. For instance, if we consider a function F(x) and its derivative is denoted as f'(x), we can find the antiderivative by integrating f'(x) with respect to x.
Antiderivative Class 12 Mathematics Solutions PDF
This PDF will provide you each and every question solutions for the 3rd exercise of class 12 antiderivatives chapter. If you want the solutions of other exercises then you can click on the respective exercises from above button.
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Standard Integrals (I)
In this section, we discuss some integrals which are directly related to standard differentiation formulae and so may be considered as some of fundamental integrals.
Some Integrals Reducible to Standard Forms
The integrals of the forms ∫1/(a * x² + bx + c) dx and (dx)/(sqrt(a * x² + bx + c)) can now be easily evaluated by converting them into above standard integrals as illustrated in the worked out examples below.
The other forms of integrals which can be reduced to the standard integrals are;
What does the solutions PDF contains?
Some people who haven’t downloaded the solutions PDF may be wondering what the PDF contains. If that’s the case, then you don’t need to worry. I’ll tell you exactly what the PDF contains. The PDF essentially includes the solutions to all the questions provided in the third exercise. If you’re unsure about the types of questions given in the exercise, you can scroll down to access them.
- Integrate 1/(a²sin²x + b²cos²x)dx
- Integrate 1/[(sinx.cosx)²] dx
- Integrate 1/(4 – 5sin²x) dx
- Integrate (cos x – sin x)/[sqrt(sin 2x)] dx
- Integrate 1/(3sin x – 4cos x) dx
- Integrate (sin 2x)/[(sin x + cos x)²] dx
- Integrate 1/(2 + cosx) dx
- Integrate 1/(1 – 2cos x) dx
- Integrate 1/(1 – 2cos x) dx
- Integrate 1/(1 + sinx + cosx) dx
- Integrate 1/(2 + 3cos x) dx
- Integrate 1/(1 + 2sin x) dx
- Integrate 1/(2 + sin x) dx
- Integrate 1/(sin x + cos x) dx
- Integrate 1/(3sin x + 4cos x) dx
- Integrate tanh(x) * 1/[cosh(x) + 64sech(x)] dx
- Integrate sinh(x) * 1/[4tanh(x) – cos echx.sech(x)] dx
- Integrate 1/[4 + 3cosh(x)] dx
- Integrate 1/[4 + 3sinh(x)]dx
The PDF given above contains the solutions of all 19 questions listed. The PDF also contains the formula needed to solve the questions of this exercise. Now I think you all are clear about what does the PDF contains. We have created all the notes and PDF without lots of hardwork and we want you to use the PDF wisely for educational purposes.
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