The derivative problem of high integral has a graph.

Suppose Ф (x) = ∫ (a to x)f(t)dt, if f is continuous, then Ф (x) is differentiable.

And Ф' (x) = f (x) ★

② From this, we can understand the second equal sign of the red line 1.

③ The derivative problem of f (x) = ∫ (0 to x 2) f (t) dt is solved according to the derivative of the compound function:

F(x) is decomposed into F(u)=∫(0 to u)f(t)dt and u = x 2,

Then, according to the derivative rule and formula of composite function, it is obtained.

F' (x) = f' (u) * u' (x) = f (u) * 2x = f (x 2) * 2x, this understanding.

(4) The upper limit is the square of x, and the lower limit is sinx. The solution is:

Using the property of integral ∫(a to B) ... =∫(a to c)...+∫(c to b)...▲ To solve,

Where ∫(sinx to c)...= -∫(c to sinx) ..., and c is a constant.

To sum up, these problems have been solved.