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Integration of even function over a symmetric intervalcan be simplified as follows: $\int_{-a}^{a} f(x) \, dx = 2 \int_{0}^{a} f(x) \, dx$ This simplification is possible because the area under the curve from $-a$ to $0$ is the same as the area from $0$ to $a$ due to the symmetry of the function. Example 1$\int_{-a}^{a} […]
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Integration of sin x cos x dx can be found using various integration technique like integration by substitution, Integration by partial fraction along with trigonometric identities. The various formula for integration of sin x cos x dx are I \[\int \sin(x) \cos (x)\, dx = -\frac {1}{4} \cos (2x) + C\] II \[\int \sin(x) \cos
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For integration of $\log(\sin x)$, we generally consider the definite integral over the interval from 0 to $\pi/2$ To calculate the definite integral of $\log(\sin x)$ from (0) to $\pi/2$, we use a technique involving symmetry and the properties of logarithms. The integral is: \[\int_{0}^{\pi/2} \log(\sin x) \, dx\] Let $I=\int_{0}^{\pi/2} \log(\sin x) \, dx$
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1) First and most important things is calmness and relaxness, Be relax and reach the examination before time. Keep a positive attitude throughout the whole test and try to stay relaxed. If you start to feel nervous take a few deep breaths to relax.
2) Dont just start the paper as soon you get it. Do some planning. When you first receive your test, do a quick survey of the entire test so that you know how to efficiently budget your time.
3) Be Time Efficient. Watch the clock. Don’t spend a huge amount of time trying to get the points for one problem! If you spend too much time trying to get the points for one problem, you may not be able to finish the exam and lose more points than you gained by taking all that time for that one problem.
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1)First thing you need to do is leave worries and tensions from your mind. Have a clear and confident mind.
2) Try Yoga.Yoga increases physical and mental abilities .This would be a great way to achieving peace of mind which charges your memory and supports physical health
3) Studies also shows that running ,doing intense exercise also help
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1. Find a place where you go only to study. It should be quiet area .Identify your distractions. Find ways to decrease them or to postpone them until study breaks e.g., taking the phone off the hook, turning off Whatapps. If using a computer, exit out of email and messengers.
2. Always sit straight in a chair at a desk, start out with questions about the material, outline chapters, underline key phrases after reading section, write notes in margins, ask yourself what you have learned.Take good notes of the chapter and revise them also.If you have difficulty understanding any thing ,search it in other books and internet. If it is not resolved,write it down to discuss with Friends and teacher
3) Doing a big task may seems to be impossible to you. So Divide your work into smaller manageable tasks that can be completed in a short period of time. First Push yourself to complete one small task, then move on to the next task. Focus on one small task at a time.
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Things to remember
1) Law of conservation of Momentum. The total momentum for the isolated remains constant
2) Elastic collision: In this collison, Momentum and Kinetic energy of the system remains conserved
3) Inelastic collision: In this collision ,Momentum is conserved only
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1) Find a good study spot .A place with a lot of distractions makes for a poor study area.A quiet place with no distraction would be good study place.
2) Take good Notes. Read through your materials slowly and write down key points. Write down any questions you have about the materials that you can later discuss with your classmates or course instructor.Quiz yourself on the material you have just read. If you struggle with certain questions, make not of these areas for additional study.Summarize the Main Points .Once you have studied the material, see if you can answer these questions: Can you identify the main concepts covere
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