58. answer 1 and 4 only, do like this example way 58 DEFINITE INTEGRALSTUTORIAL 58If fr(x) dxx) dx = 3, evaluate [1 + 2 f(x)] dx using the properties of integral2. If f(x) dx = = -2 and if f(x) dx = 1, evaluateS[x-2f(x)]dxdx using the0properties of integral.3. If f(x) dx = 5 and f(x) dx = -2, evaluate √ [x² + 2-3 f(x)]dx-1using the properties of integral.If f(x) dx = 5 and if g(x) dx = -3, evaluate [f(x) + 2g(x)]*xusing the properties of integral.If f(x) dxf(x) dx = 2 and if g(x) dx = 10, evaluate [3 f(x) - g(x)]dxusing the properties of integral.16. If Sf(x) dx = 2 and if Sg (x) dx = -3, evaluate [f(x) - 2g (x) - 4x²]07.Given f(x) dx = 10, $f(x) dx = 7₁ g(x) dx = 5.7.Evaluate Sf(x) dx - S(f(x) - 2 g(x)) dx.= -1.28. Given g(x) dx = 3, g(x) dx = 7 and00€ 601 dy5.Sf(x) dx Given •Sf(x) dx = = -2 and 1(x) dx = 1, findf(x) dxS[31(x) + x1dx$f(x) dxSf(x) dx +-/1(x) dx + 10-(-2) + 13b)dx$131(x) + x16x=3/1(x) dx + xdxv253 (1) + []X=6=- 3+251=152Example 3: If f(x) dx == -5 andf(x) dx-1.2S[f(x) = kx] dx = 7, using the properties of integral.-1Solution:[f(x) - kx]dx7f(x) dx - kĵx dx = 7-1Sf(x) dx + f(x) dx - k[]X=4= 7-1- 5 + 3 k (8-2) = 715k = 92k =b)Solution:a)=227f(x) dx= 3, find the value of k if6/51

As asked we can answer question no 1 and 4 as below.

1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and if f(x) dx = 1, evaluate S[x-21(x)] dx using the 0 properties of integral. 3. If ff(x) dx = 5 and f(x) dx = -2, evaluate [×² + 2-3 f(x)]dx using the properties of integral. 4. If Out If ff(x) dx = 5 and if g(x) dx = -3, evaluate [f(x) + 2 g(x)]dx -1 using the properties of integral.