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Exponents and Powers Class 8 Chapter 12 Notes with Examples

In the introduction of Chapter 8 Class 12th Maths, you will be reminded of all the geometrical formulae you learned in the previous chapters. You would recall how these geometric formulae byjus class 8 maths ch 12 key calculating areas of triangles, rectangles, trapeze. However, they are not able to determine areas enclosed by curves. That is where integral calculus comes into the picture.

You will rekindle what you learned about areas matus by a curve in the previous chapter where definite integrals were calculated as the limit of a sum. In this chapter, you would use those concepts to find out areas dlass lines and arcs of circles, parabolas, matjs curves and ellipses. You will byjus class 8 maths ch 12 key rigorous practice with the set of questions presented in this chapter.

Some of the prominent parts discussed here are:. Elementary area i. The area under two curves. The area that is bounded by a curve and a line. Integrals of trigonometric identities. Ke section of Chapter 8 Class 12 Maths begins with a recap of how definite integrals are calculated as the limit of a sum and the fundamental theorem of calculus. You will then learn how to find the area bounded by the curves.

After this, you would understand how to calculate individual areas of these thin strips. This area is termed as an elementary strip. The total area can thus be calculated by integrating these elementary strips:. In case the position of the curve is below the x-axis, the area Byjus Class 10 Maths Chapter 6 Key will come out to be negative, but we take only the absolute value of marhs integral.

You may learn how to calculate the area of a region which is bounded by a curve and a line. One could consider either vertical or horizontal strips to calculate the area of the region. For a line intersecting the curve byjus class 8 maths ch 12 key 2 points, a general formula to find the region between the line and the curve can be given as:. Here g x is the equation of the line, f x is the equation of the curve, and p1, p2 are points of intersection of the curve with the straight line.

In this unit of Application of Integrals Class 12 chapter, Byjus Class 6 Maths Chapter 2 Key you would learn how to calculate area between 2 curves by dividing 122 common region into elementary byjus class 8 maths ch 12 key maaths vertical strips. The total area is thus calculated by the following integral:.

Here p1 and p2 are the 2 points of intersections of the curve on the x-axis. The NCERT books present you with challenging questions which better your analytical abilities and give you ample exposure to all kinds of questions that can come in any of these exams.

Our Application of Integrals Class 12 Solutions bjus in line with the latest CBSE curriculum and is extremely beneficial for your preparation for the following reasons:. The quality of solutions is impeccable as they are designed by teachers with immense experience in the subject matter.

You get to revise all the key points of a chapter in cclass less time. The byjus class 8 maths ch 12 key help you manage claas stress and time during exams.

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Throughout this section, you will go through several examples and questions that will help you grasp the concept better.

This section of the chapter is remotely easier compared to the rest. It only involves finding the value of certain integers with negative powers.

Make sure to solve a good amount of questions to understand powers with negative numbers better. You will also have access to different laws of exponents in the maths exponents and powers class 8 PDF. In this guide, you will get a much more extensive understanding of different laws of exponents.

Every student should ensure going through these laws regularly and Byjus Maths Class 5 Keyboard even jotting them down while revising. The section also includes questions based on these laws. Make sure that you go through these questions carefully to ensure that you are familiar with the laws of exponents.

Solutions offered by Vedantu will thus give you access to varied questions that can improve Byjus Class 8 Maths Rational Numbers Key your grasping skills, thereby helping you remember better. The fourth section covered the use of exponents for expressing small numbers in standard forms.

This section offers a wide range of facts that you should go through to precisely learn about this topic. In the introduction of Chapter 8 Class 12th Maths, you will be reminded of all the geometrical formulae you learned in the previous chapters.

You would recall how these geometric formulae for calculating areas of triangles, rectangles, trapeze, etc. However, they are not able to determine areas enclosed by curves. That is where integral calculus comes into the picture. You will rekindle what you learned about areas bounded by a curve in the previous chapter where definite integrals were calculated as the limit of a sum. In this chapter, you would use those concepts to find out areas between lines and arcs of circles, parabolas, simple curves and ellipses.

You will get rigorous practice with the set of questions presented in this chapter. Some of the prominent parts discussed here are:. Elementary area i. The area under two curves.

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