试题来源: 解析 (dx)/(f(x)) = √(1-x^2)dx 由已知积分表达式 ∫ xf(x)dx = arcsin x + C,对等式两边求导,得 xf(x) = 1/(√(1-x^2))。 因此,f(x) = 1/(x√(1-x^2)),则 (dx)/(f(x)) = x√(1-x^2)dx。反馈 收藏 ...
【题目】证明:若函数f(x)在[0,+∞)一致连续,且无穷积分$$ \int _ { 0 } ^ { + \infty } $$f(x)dx收敛,则$$ \lim _
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∫14+sinxdx=13log |f (x)| + c then f(x) =
Answer to: Find \int f(x) dx in terms of x given the following \int f(x)dx = \theta + \tan \theta - \ln(\sec \theta) + C, \sin \theta =...
解析 本题考查了定积分求导问题,需要学生熟练掌握定积分求导公式;根据题意,首先求得∫f(x)dx的导数;接下来再对上一步求得的导数进行求导,即可得到答案.C.∵∫f(x)dx=F(x)+C,∴[∫f(x)dx]'=F'(x)=f(x),∴d∫f(x)dx=f(x)dx.故选C. ...
lnx)dx =∫(x+xlnx)dx =1xdx+∫xlnxdx =1/2x^2+1xlnxdx =1/2x^2+1/2x^2lnx-√(1/2)x^21/xdx :(1/2x^2lnx)'=xlnx+1/2x^2-1/x] F 1 =1/2x^2+1/2x^2lnx-1/4x^2+C ∴∫(xlnx+1/2x^2-1/x)dx=1/2x^2lnx ∴∫xlnx=1/2x^2lnx-∫1/2xdx =1/2x^2lnx-1...
यदि int f(x) dx = g(x) + c हो, तो int f^(-1) (x) dx बराबर है
If 2f(x)−3f(1/x)=x, then ∫21f(x)dx is equal to A(3/5)log2 B(−3/5)(1+log2) C(−3/5)log2 DNone of theseSubmit If ∫4−1f(x)dx=4and∫42(3−f(x))dx=7, then ∫2−1f(x)dx= A−2 B3 C4 D5Submit If f(x)+f(2−x)=0, then ∫2011+2f(x...
Answer to: Evaluate \int^c_b f(x) dx, given \int^c_a f(x)dx=2, \ \int^b_cf(x)dx=-5 By signing up, you'll get thousands of step-by-step solutions...