Antiderivative ဟာ Grade 12 သင်ရိုးတွင် ပြဌာန်းလာမည့် သင်ခန်းစာတစ်ခုဖြစ်ပါတယ်။ သင်ခန်းစာရှင်းလင်းချက်များကို ဒီနေရာမှာ ရေခဲ့ဖူးပါတယ်။ အဆိုပါ post နှင့် ယှဉ်တွဲလေ့လာပြီး အောက်ပါ လေ့ကျင့်ခန်းများကို လေ့လာ လေ့ကျင့်ကြည့်နိုင်ပါတယ်။ စဉ်ဆက်မပြတ် လေ့လာသင်ယူနိုင်ကြပါစေ။
Rules of Integration
1. ∫k dx=kx+c 2. ∫f′(x) dx=f(x)+c 3. ∫xn dx=xn+1n+1+c 4. ∫kf(x) dx=k∫f(x) dx 5. ∫[f(x)±g(x)] dx=∫f(x) dx±∫g(x) dx |
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- Integrate each of the following with respect to x.
(a) x3
(b) 3√x
(c) 2x2
(d) 12√x
(e) (3x+5) dx - Find each of the following indefinite integrals.
(a) ∫(3x−1)(x+2) dx
(b) ∫(3x3−4√x+3) dx
(c) ∫(6x2−4x2) dx
(d) ∫(5−1√x+1x3) dx
(e) ∫x4+5x2x3 dx - Find each of the following indefinite integrals.
(a) ∫3x25√x2 dx
(b) ∫(3x−1)25x4 dx
(c) ∫3x7+x223√x dx
(d) ∫(x−3√x)2 dx
(e) ∫(1+4√x)(1−4√x)dx
(f) ∫(3√x+23√x)2 dx - The rate of change of A with respect to r is given by dAdr=4r+7. If A=12 when r=1,find A in terms of r.
- Given that the gradient of a curve is 2x^2 + 7x and that the curve passes through the origin, determine the equation of the curve.
- A curve is such that \dfrac{dy}{dx}=k\sqrt[3]{x} , where k is a constant and that it passes through the points (1, 4) and (8, 16). Find the equation of the curve.
- The gradient of a curve at the point (x, y) on the curve is given by \dfrac{x^{2}-4}{x^{2}}. Given that the curve passes through the point (2,7), find the equation of the curve.
- A curve with \dfrac{dy}{dx}=k x+3, where k is a constant, passes through the point P(3,19). Given that the gradient of the normal to the curve at the point P is -\dfrac{1}{15}, find
(i) the value of k,
(ii) the equation of the curve,
(iii) the coordinates of the turning point on the curve.
- The equation of a curve is such that \dfrac{dy}{dx}=\dfrac{1}{(x-3)^{2}}+x . It is given that the curve passes through the point (2,7). Find the equation of the curve.
စာဖတ်သူ၏ အမြင်ကို လေးစားစွာစောင့်မျှော်လျက်!