Finding the Integral Upline 1 Downline 0 cosx 2 dx

Question 1 (cosx+2)dx= cosxdx+ 2dx=-sinx+c1+2x+c2

Question 2 (Upper Limit 1 Offline 0) (2x 4+4x 3+x 2+1)dx

Cap 1 Downline 0) 2x 4DX+ Limit 1 Downline 0) 4x 3DX

Upper limit 1 downline 0) x 2dx + upper limit 1 downline 0) dx

2 5 * (x 5)] (upper limit 1 offline 0) + [4 4 * (x 4)] (upper limit 1 offline 0).

1 3*x 3] (upper limit 1 offline 0) + [x] (upper limit 1 offline 0).

The integral is actually the inverse process of finding the derivative, for example, the x 5 derivative is 5*x 4∫(5*x^4)dx=x^5+c

c is a constant because its value cannot be determined. There is also the sinx derivative which is cosx∫cosxdx=sinx+c.

The upper and lower limits of the definite integral are to substitute the lower limit with the upper limit after finding the integral, which is related to the area finding method of the definition of the definite integral, which is not easy to say, just know the meaning.

To solve the indefinite integral, the constant c. must be addedMy answer c1+c2 is just to make the answer clearer, and it can also be made.

c=c1+c2.But it is important to understand that the value of c is not the same for each indefinite integral.

Question 3 Derivative, y=x(-2 3)(minus thirds of x) y =(-2 3) *x(-5 3)(minus 5/3 of x) So when x0=1, y0=1 y =-2 3 is the slope of the tangent Use the point oblique to find the tangent.

y-y0=y (x-x0) The tangent equation is y+2 3* x-5 3=0

Solution:1∫(cosx+2)dx

cosxdx+∫2dx

sinx+2x+c

2.(2x 4+4x 3+x +1)dx(2 5)x 5+x 4+(1 3)x 3+x+c, bring in the upper and lower limits [0,1] to obtain the original formula = 41 15

LS miscalculated, happy studying!

Summary. Hello dear, split into two items, the first term is the definite integral of the odd function on the symmetry interval, which must be 0. The second primitive function is (1 2)e 2x, and the answer is (1 2)[e 4-e (-4)].

Finding the definite integral (up and down 0) (2x+cosx+e on 2x)dxHello dear, split into two items, the first term is the definite integral of the odd function on the symmetry interval, this feast must be 0. The original function of the silver term in the second forest file is (1 2)e 2x, and the answer obtained by substituting the upper and lower bounds of the stupid macro is (1 2)[e 4-e (-4)].

Upper limit 2, lower vertical middle limit 0) e (2x)cosxdx= (upper limit 2, lower limit 0) e (2x)d(sinx) =e 2 (upper limit 2, lower limit 0) e (2x)d(cosx) =e 2 - 4 (upper limit 2, lower limit 0) e (2x)cosxdx Therefore, Yu Blind Mountain: (upper limit 2, lower limit 0) e (2x)cosxdx=(e 2) 5

-1≤sinx≤1

sinx+1≥0

Therefore, the difference between sinx+1 and the difference between the sail base car and the difference dx= sinx+1)dx=[x-cosx] =2

Summary. The upline is 1, the downline is -1, and the cosx+sinx 3 is a definite integral.

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Stupid with sinx (1+cosx 2)dx=- 1+cosx 2)dcosx with y=cosx, there is =- 1+y 2)dy=-y 2* (with key 1+y 2)-1 2*ln(y+ (1+y 2))+c and y=cosx, substitute back; Sell guess = -cosx 2* (1+cosx 2)-1 2*ln(cosx + (1+cosx 2))+c....