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# Integration Formulas for Class 12

Students in early grades learn how to determine the areas of various geometrical shapes using some elementary geometry methods. These methods and formulas are fundamental to learning multiple applications of mathematics in real-life problems. However, to determine the areas covered under a curve we need integration formulas. Integration formulas for class 12 are useful in determining the area covered under a curve and between two curves. These formulas are important to solve a variety of questions based on integration by using different methods. Apart from mathematics, these integration formulas for class 12 are applied to solve scientific and engineering problems.

## List of Integration Formulas for Class 12

Here is the list of integration formulas for class 12:

- ∫ f(x) dx = F(x) + C
- Power Rule: ∫ x
^{n}dx = (x^{n+1})/ (n+1)+ C. (Where n ≠ -1) **Exponential Rules: ∫ e**^{x}dx = e^{x}+ C

∫ a^{x} dx = a^{x}/ln(a) + C

∫ ln(x) dx = x ln(x) -x + C

- Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant.
- Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C
- Sum and Difference Rules:

∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx

∫ [f(x) - g(x)] dx = ∫f(x) dx - ∫g(x) dx

- ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
- Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫[d/dx f(x) * ∫ g(x) dx]dx
- ∫cos x dx = sin x + C
- ∫ sin x dx = -cos x + C

- ∫ sec
^{2}x dx = tan x + C - ∫ cosec
^{2}x dx = -cot x + C - ∫ sec x tan x dx = sec x + C
- ∫ cosec x cot x dx = - cosec x + C
- Area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) : a∫b y dx = a∫bf(x) dx.
- Area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d : c∫d x dy = c∫d φ (y) dy.
- Area of the region enclosed between two curves y = f (x), y = g (x) and the lines x = a, x = b : b∫a[f(x) - g(x)] dx

## Applications of Integration Formulas for Class 12

Integration formulas for class 12 are applied in mathematics to determine areas, volumes, central points and many other useful aspects related to a non-uniform curve with some given function. Here are a few examples of real-life applications of these integration formulas for class 12.

- Integration formulas for class 12 are used in physics to calculate the center of gravity, mass and momentum of inertia of vehicles.
- These formulas are also applied to calculate the mass and momentum of satellites or a tower.
- The application of these formulas can be found in finding the velocity and trajectory of a satellite at the time of placing it in orbit.

## Tips to Memorize Integration formulas for class 12

The following tips can be helpful for the students to remember the integration formulas for class 12:

- Students must have a clear understanding of the underlying logic of all formulas for easing the memorization process.

- It is better to clarify all doubts before trying to memorize integration formulas for class 12. Eliminating all doubts at the start will help in memorizing these formulas better.

- Students should try to solve several problems based on integration formulas for class 12 to get familiarized with the usage of these formulas in different scenarios. This will allow students to recall them quickly when required.

- Students can use various resources like formula sheets available on the internet to revise these integration formulas for class 12.

## Integration Formulas for Class 12 Examples

**Example: **Find the integral of Sin2x.

**Solution:** We know that, d/dx(Cos2x) = - 2Sin2x

⇒ Sin2x = -½ d/dx(Cos2x)

⇒ Sin2x = d/dx(-½ Cos2x)

Thus the integral or anti-derivative of Sin2x = -½ Cos2x.

Students can download the printable **Maths Formulas class 12** sheet from below.

## FAQs on Integer Formulas for Class 12

### What are the Important Integration Formulas for Class 12?

The important Integration formulas for class 12 are listed below:

**Exponential Rules:****∫ e**^{x}dx = e^{x}+ C

∫ a^{x} dx = a^{x}/ln(a) + C

∫ ln(x) dx = x ln(x) -x + C

- Constant Multiplication Rule: ∫ a dx = ax + C, where a is the constant.
- Reciprocal Rule: ∫ (1/x) dx = ln(x)+ C
- Sum and Difference Rules:

∫ [f(x) + g(x)] dx = ∫f(x) dx + ∫g(x) dx

∫ [f(x) - g(x)] dx = ∫f(x) dx - ∫g(x) dx

- ∫k f(x) dx = k ∫f(x) dx, , where k is any real number.
- Integration by parts: ∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫[d/dx f(x) * ∫ g(x) dx]dx

### What are the Basic Integration formulas for class 12?

Some of the basic integration formulas for class 12 are listed in this article. Students can try to derive and apply them in various questions. It will help them to implement them better. In addition to that students can follow the tips and tricks mentioned above to memorize these formulas better.

### How Many Formulas are Covered in Integration Formulas for Class 12?

There are around 20 to 30 main formulas covered under integration formulas for class 12 which, if memorized well, will enable students to solve various problems covered under integration calculus. Memorizing these formulas is also important for the preparation of various competitive exams.

### How to Memorize Integration Formulas for Class 12?

To memorize Integration formulas for class 12 the students can use the following tips:

- Thoroughly read the theory and content presented in the chapter thoroughly and note down all the doubts so as to get them cleared with the help of teachers or friends. If the basics will be clear there will be no difficulty in understanding the formulas.

- Once the theoretical part is clear, the students must try to do all the solved examples and then move to the exercise questions. This will help in giving a good practice of the usage of the formulas in different contexts.

- Students can also take the help of their mobiles and laptops in the learning process. The images of formulas can be set as wallpaper on these devices to ensure having a glance at them throughout the day.

### How to Download Integration Formulas for Class 12?

To download the integration formulas for class 12 click on the download option provided on this page. After clicking this option a popup will appear to enter your phone number. Enter your number and OTP received to download the formula sheet.

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